# The first term of an infinite geometric progression is 1 and the sum of the terms is 13, find common ratio.

25,598 results
1. ## Maths

The 3rd and 4th term of geometric progression are 4 and 8 respectively find: The first term and common ratio, The sum of the first 10 term, The sum of infinity.

2. ## Arithmetic

The first, second and third terms of a geometric progression are 2k+3, k+6 and k, respectively. Given that all the terms of geometric progression are positive, calculate (a) the value of the constant k (b) the sum to infinity of the progression.

3. ## quine

The 2nd and 5th term of a geometric progression are - 6 & 48 find the sum of the first four term respectively

4. ## math

Find the third term and the sum of the first 30 terms of the geometric progression 2, 3, ...

5. ## mathematics :geometric progression

The first three terms of a geometric progression are K-3,2K-4,4K-3 in that order find the value of K and the sum of the first 8 terms of the progression

6. ## Mathematics

The 5th and 10th terms of an arithmetic progression are 18 and -2 respectively. (a) Find the common difference and the first term. (b) Determine the least number of terms which must be added together so that the sum of the progression is negative .Hence

7. ## math

The 3rd term of an Arithmetic Progression is 10 more than the first term while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the Arithmetic Progression if the 7th term is seven times the first term.

8. ## math

Find the sum to 5 terms of the geometric progression whose first term is 54 and fourth term is 2

9. ## Maths

1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is 4/3 less than the sum of

10. ## math

The first, the third and the seventh terms of an increasing arithmetic progression are three consecutive terms of a geometric progression. In the first term of the arithmetic progression is 10 find the common difference of the arithmetic progression

11. ## Math

1. Find the 11th term of the geometric sequence 64, -32, 16, -8, … . 2. Find the 1st term of a geometric sequence with a 10th term -1024 and r = -2. 3. Find the sum of each infinite geometric series, if possible. a. 10 + 2 + 2/5 + ..... b. 1.2 – 2.4 +

12. ## Math

a geometric progression has a third term of 20 and a sum to infinity which is three times the first term. find the first term

13. ## Mathematics

The sum of the geometric progression a,ar,ar^2,ar^n-1 is S the product of these n term s is P. Find R,the sum of the reciprocals of these n term s and show that (S/R)^n=P^2

14. ## Math

The third, fifth and seventeenth terms of an arithmetic progression are in geometric progression. Find the common ratio of the geometric progression.

15. ## Math

The common ratio of a geometric progression is 1/2 , the fifth term is 1/80 , and the sum of all of its terms is 127/320 . Find the number of terms in the progression.

16. ## Maths

a geometric progression has the second term as 9 and the fourth term as 81. find the sum of the first four terms.?

17. ## mathematics

in a geometric progression, the first term is a and the common ratio is r. the sum of the first two terms is 12 and the third term is 16. a) determine the ratio (ar^2)/a+ar( aready found the answer as 4/3) b) if the first term is larger than the second

18. ## Maths

The numbers p,10 and q are 3 consecutive terms of an arithmetic progression .the numbers p,6 and q are 3 consecutive terms of a geometric progression .by first forming two equations in p and q show that p^2-20p+36=0 Hence find the values of p and q for

19. ## Math

Three numbers form a geometric progression. If 4 is subtracted from the third term, then the three numbers will form an arithmetic progression. If, after this, 1 is subtracted from the second and third terms of the progression, then it will again result in

20. ## math

An arithmetic progression as the same first and second terms as the geometric progression. Find the sum of the first 20 terms of the arithmetic progression. How do I do this? I tried to find the common ratio for G.P. and then substitute it to find the 20th

21. ## Algebra

The first term of an A.P is 3 and the fifth term is 9.Find the number of terms in the progression if the sum of the progression is 81.

22. ## Maths

A Geometric progression X has a first term of 4a and its sixth term is 256. Another Geometric progression Y has a first term of 3a and its fifth term is 48. Find the: (i) First term of X (ii) Sum of the first four terms of X

23. ## math

1)Find the sum of the first eight terms of the Geometric progression 256,128,64,32 2)How many terms should be taken from the Geometric progression 4,12,36 for the sum to be 2188

24. ## maths

the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and 9th terms of the progression is 52. find the first term, the common difference and the sum of the first ten terms of the progression.

25. ## Math

The third term of a geometric progression of positive terms is 18 and the fifth term is 162 Find the common ration and the first term? Write an expression for the Nth term of the progression? Find the sum of the first 8 terms of the progression??

26. ## Algebra 2

Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first four terms of the sequence? a{1} = first term of series ∞ Infinite Sum = ∑ a{1} • r^(n – 1) = a{1} ⁄ (1 – r) ... for any geometric series

27. ## math

The third,sixth and seventh terms of a geometric progression(whose common ratio is neither 0 nor 1) are in arithmetic progression. Prove dat d sum of d first three is equal to d fourth term

28. ## Math

The second and fifth terms of a geometric progression (G.P) are 1 and ⅛ respectively. Find the: A, common ratio; B, first term; C, eighth term.

The first term and second term of a geometric progression are 16 and 2 respectively, Find the sum to infinity of the progression

30. ## math

for the geometric progression 20,5,1and half. find (1)the common ratio (2)the n the term (3)the sum of the first 8 term

31. ## Math

The sum of the 4th and 6th terms of an AP is 42. The sum of the 3rd and the 9th term of progression is 52, find the first term and the common difference of the sum of the 1st, 10th terms of the progression

32. ## math

A certain infinite geometric series has first term 7 and sum 4. What is the result when the third term is divided by the second term?

33. ## GP Caluculus

The third term of a geometric progression is 16. The sum of the third term and the fouth term is 8. Find (a)the first term and the common ration of the progression (b)the sum of infinity of the progression

34. ## AP Calculus

The 9th term of an arithmetic progression is 4+5p and the sum of the four terms of the progression is 7p-10, where p is a constant. Given that common difference of the progression is 5, find the value of p.

35. ## Math *URGENT

Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 3. Determine the geometric mean of 8

36. ## mathematics

In a geometric progression with terms, the sum of the first and last term is 66 and the product of the second and second last term is 128. Given that the sum of all the terms of this geometric progression is 126, find the number of terms and possible

The eighth term of a geometric progression is 32 and the fourth term is 2. Find the first term and the positive value of the common ratio b) find the sum to infinity of a geometric progression whose first term is 5 and second term is -4 c) The nth term of

38. ## algebra

if 1, 2, 7 and 20, respectively, are added to the first terms of an arithmetic progression, a geometric progression of four terms is obtained. find the first term and common difference of the arithmetic progression the answers are both 3 .. but i don't

39. ## GP Caluculus

The third term of a geometric progression is 16. The sum of the third term and the fourth term is 8.Find (a)the first term and the common ratio of the progression. (b)the sum of infinity of the progression.

40. ## GP Caluculus

The third term of a geometric progression is 16. The sum of the third term and the fouth term is 8. Find (a)the first term and the common ration of the progression (b)the sum of infinity of the progression

41. ## Geometric progression

The second term of a geometric progression is 12 more than the first term given that the common the ratio is half of the first term. Find the third term of the Geometric progression

42. ## maths

In an arithmetical progression,the sum of the first five terms is 30,and the third term is equal to the sum of the first two.write down the first five terms of the progression.

43. ## math

The product of the first five terms of a geometric progression is 32. If the fourth term is 17, compute the second term.

44. ## math C2 sequences and series

The eight,fourth and second terms of an arithmetic progression form the first three terms of a geometric series. The arithmetic progression has first term A and common difference d, and the geometric progression has first term G and common ratio r. a)Given

45. ## arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four

46. ## arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four

47. ## math

An infinite geometric series has a first term of \$12\$ and a second term of \$4.\$ A second infinite geometric series has the same first term of \$12,\$ a second term of \$4+n,\$ and a sum of four times that of the first series. Find the value of \$n.\$

48. ## Math

Given a geometric progression: 0.05, 0.2, 0.8, ... Find the sum from the 5th term to the 8th term?

49. ## Algebra 2

In an infinite geometric progression with positive terms and with a common ratio |r|

50. ## plz sequence sir steve reiny bob damon i need u

The three real,distint and non-zero numbers a,b,c are such that a,b,c are in arithmetic progression and a,c,b are in geometric progression. Find the numerical value of the common ratio of the geometric progression.. Hence,find an expression in terms of a

51. ## Math

Find the sum to 5 terms of the geometric progression whose first term is 54 and fourth term is 2.

52. ## Math

Find G1 in geometric progression for which the sum of 1st two terms is -4 and the fifth term is 4 times the third term. If the common ratio is postive

53. ## maths

1) The first term of arithmetic progression is -20 and the sum of it's term is 250. find it's last term if the number of it's terms is 10 2) Find the fifth term from the arithmetic progression -12, -9, -6 hence find the sum of it's first fifty terms. 3)

54. ## maths

The first three terms of an arithmetic-geometric progression are 3, –1 and –1. The next term of the progression is

55. ## Math

Given a geometric progression whose common ratio is 2, if the sum of the 6th to 7th terms is 288, determine the sum of the 4th to 15th terms inclusive.

56. ## Math

4) The sum of an infinite geometric series is 100. The second term of the series is 24. Find two possibilities for a (the first term) and r (the common ratio). b. Given, 5 2 4 a a a    159 and 4 1 3 a a a    265 , find the terms of the

57. ## Math

A certain infinite geometric series has first term 7 and sum 4. What is the result when the third term is divided by the second term?

58. ## Algebra

Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|

59. ## math

If the sum of the first and the second terms of an infinite Geometric progression is equal to 3/8, and the sum of its term is equal to 1/2. find the common ratio of the first term of the progression

60. ## Math (Geometric Progression)

5 distinct positive reals form an arithmetic progression. The 1st, 2nd and 5th term form a geometric progression. If the product of these 5 numbers is 124 4/9, what is the product of the 3 terms of the geometric progression? Note: The phrase "form an

61. ## Math

The common ratio of a geometric progression is 1/2 , the fifth term is 1/80 , and the sum of all of its terms is 127/320 . Find the number of terms in the progression.

62. ## math

The sum of the 3 terms in arithmetic sequence is 39.if these numbers is increased by 1,5 and 12 respectively the numbers would be in geometric progression. find the second term of the geometric progression?

63. ## Pre-Calculus

Q.Determine the sum of each infinite geometric series. t_1= 8 r = -2^1/2 ---------------------------------------- A.This is a divergent series because the absolute value of r is greater than 1. ---------------------------------------- Q. The first term of

A geometric progression has a first term of 6 and a common ratio of -3. Find the sixth terms of the progression.

65. ## Mathematics

an exponential sequence (geometric progression) has first term x and common ratio x ,x≠1 write down the sum of the first n terms of this sequence (1a): write down the sum of the first n terms of this sequence (1b): |x|infinity (1c): if An=sum r=1 to n

66. ## math

I would need help with example: The sum of three consecutive terms of geometric progression is 9. The first number with no change, the second number plus 12 and the third number minus 3, are the 3 consequtive terms of arithmetic progression. What are the

67. ## A.P AND G.P AND A.M AND G.M

Find the arithmetic progression and sum of its first 20 terms whose arithmetic mean and geometric mean between first and third term is 10 and 8 respectively

68. ## Maths

A geometric progression has a third term of 20 band sum to infinity which is three times the first term. find the first term.

69. ## Mathematics

The 25 term of an Arithmetic Progression is 7 1/2 and the sum of the first 23 terms is 98 1/2. Find the i. 1st term ii. common difference iii. sum of the first 30 terms

70. ## intro cal

the first 3 term of a geometric progression are k-4, 2k-4, 4k+4. what is the value of k? can someone help please! in any geometric progression any term divided by its previous term gives you the common ratio, so .... (2k-4)/(k-4) = (4k+4)/(2k-4)

71. ## Series

One sequence of alternating terms of the series 1+2+3+4+5+8+... forms an arithmetic progression, while the other sequence of alternating terms forms a geometric progression. Sum the first 10 terms of each progression and hence find the sum of the first 20

72. ## Mathematics

If the sixth term of an arithmetic progression (A.P) is 37 and the sum of the six term is 147, find the first term, common difference, sum of the first fifteen terms

73. ## algebra 2

An arithmetic progression has 5 terms that have a sum of 200. The sum of the last three terms added to 6 times the sum of the first two terms equals zero. What is the first term?

74. ## Algebra

In an infinite geometric progression with positive terms and with a common ratio |r|

75. ## Geometric progression

The first term of an infinite geometric progression is 1 and the sum of the terms is 13, find common ratio.

76. ## math

In a geometric progression of first term 5 and common ratio 4/5, what is the minimum number of terms that must be added for the difference between the infinite sum and this sum would be less than 0.3?

77. ## math

in a Geometric progression the sum of the first and the second terms is 90 and the sum of the second and the fourth terms is equal to 30.find the sum of the first 8th term in the progression

78. ## Math

5 distinct positive reals form an arithmetic progression. The 1st, 2nd and 5th term form a geometric progression. If the product of these 5 numbers is 124 4/9, what is the product of the 3 terms of the geometric progression? Note: The phase "form an

79. ## MATHEMATIC DEPARTMENT

The second, third and ninth terms of an arithmetic progression forms the first, second and third terms of a geometric progression. Find the common ratio and hence the eleventh term of geometric progression.

80. ## math

1) If the number 1,1/3,1/9, are terms of Geometric progression. Find its common ratio 2) If the second term of Geometric progression is equal to 3, and the 5th term is equal to 81/8. Find the 7th term. 3)If x,y,3 is a Geometric progression. Find the value

81. ## algebra

Can someone please help me with this problem? Thanks! Evaluate the infinite geometric series: 8+4+2+1+... I thought you needed to know the number of terms to evaluate, but how do you know them if it is infinite? The limit of Sn = 1 + r + r^2 + r^3 + r^4 +

82. ## Mathematics

In a geometric progression,the 4th term exceeds the 3rd term by 72 and the 3rd term exceeds the 2nd term by 24. Calculate the first four terms of the progression and their sum

83. ## mathematics

What is the sum to 5 terms of the geometric progression whose first term is 54 and fourth term is 2?

84. ## mathematics

the third terms of a geometric progression is 360 and the sixth term is 1215. find the sum of the first four terms....

85. ## Mathematics

The 4th, 6th and 9th term of an arithmetical progression form the first three times of a geometric progression. If the first term of the arithmetic progression is 3 determine the common difference of the arithmetic progression and common ratio of the

86. ## Math

If the 2nd and 5th term of a geometric progression are -6 and 48 respectively. Find the sum of the first four terms.

87. ## arithmetic

Each term of a progression is determined by adding 0.5 to the preceding term. the sum of the first 25 terms of the progression equals the square of the 25th term. calculate the possible value(s) of the first term

88. ## algebra

Okay, I was taught that if a geometric series is infinite and it diverges then it has no limit and no sum. Looking back in my notes, I found an example of finding the value for a divergent series? Is this possible? The sum of an infinite geometric

89. ## mathematics

In a geometric progression, the first term is a and the common ratio is r. The sum of the first two terms is 12 and the third term is 16. determine the ratio ar^2/a+ar

90. ## Hill school

The first three terms of a geometric progression are K-3,2K-4,4K-3 in that order find the value of K and the sum of the first 8 terms of the progression.

91. ## Calculus

In calculus, the sum of an infinite geometric series whose first term is 1/20 is given by the complex fraction 1/20 _____ 1-r where r is the common ratio between the terms. Simplify this expression.

92. ## progressions

Find the arithmetic progression and sum of its first 20 terms whose arithmetic mean and geometric mean between first and third term is 10 and 8 respectively

93. ## Further maths

The sum of the fourth and sixth term of an arithmetical progression is 42.the sum of the third and the ninth term is 52.find the first term,the common difference and the sum of the first tenth term of the progression.

94. ## math

in a.p. frist term is 4 .the frist ,second and third form consecutive terms of geometric progression. find the first three terms of arithmetic progression

95. ## PreCalculus

Determine the sum of the geometric series: p+p^2+p^3+.....+(n terms) I know how to work the formulas but I don't understand how I can find 'tn'. Thanks, -Jay I'm not sure what you mean by 'tn'. Is that t_n, t-sub-n? Let's look at the case where there are a

96. ## math

in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence form the 2nd and

97. ## Math

Sum of4th and the 6th terms of an a,p is 42 . While the sum of the 3rd and 9th terms of the same a.p is 52. Find the (a) first term (b)common difference (c) sum of the first ten terms of the progression. Solution