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

Arithmetic
The sum of three consecutive terms of a geometric progression is 42, and their product is 512. Find the three terms.

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

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.

Algebra 2
In an infinite geometric progression with positive terms and with a common ratio r

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.

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

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

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^220p+36=0 Hence find the values of p and q for

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

Advanced Algebra
The arithmetic progression has first term 4 and last term 34. If the sum of its terms is 247, find the number of terms and their common difference.

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.

Mathematics
The second and fifth terms of a geometric progression (g.p) are 1 and 8 respectively. Find the common ratio,first term, and the eight term.

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

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

Math
The sum of the first nth term of a geometric progression is 127 and the sum of their reciprocal is 127/64. The first term is 1. Find n and the common ratio.

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.

Maths
1) In the arithmetic progression, the 8th term is twice the 4th term and the 20th term is 40. Find the common difference and the sum of the terms from the 8th to the 20th term inclusive. 2) Find the least number of terms of the AP, 1+3+5...that are

Mathematics
If the 2nd and 5th terms of a geometric progression are 6 and 48 respectively, find the sum of the first four terms.

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

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.

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

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

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.

Math
How do we find the sum of n terms of the series, 1+(4/7)+(7/49)+(10/343)+..... I know that it can be written as a combination of an arithmetic and geometric progression. 1=(4+3r)/(7^m) ; (r=1 , m=0) 4/7=(4+3r)/(7^m) ;(r=0,m=1) But how do we find the sum

math
find the sum of the first 8th term of the Geometric progression, 1,3,9,27

math
find the 7th term of the geometric progression if the first and 5th terms are 16 and 9 respectively.

maths
The sum of first 6 terms of an Arithmetic progression is 6 the product of 2nd term and 5th term is 80 . Find the terms of A.P.

plz sequence sir steve reiny bob damon i need u
The three real,distint and nonzero 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

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

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.

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

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

Maths
The sum of the last three terms of a G.P having n terms is 1024 times the sum of the first three terms of the progression. If the third term is 5, find the last term.

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

mathematics :geometric progression
The first three terms of a geometric progression are K3,2K4,4K3 in that order find the value of K and the sum of the first 8 terms of the progression

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

arithmetic
in an arithmetic progression the 13th term is 27 and the 7th term is three times the second term find;the common difference,the first term and the sum of the first ten terms

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

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??

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

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

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

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

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?

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

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

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

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

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.

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?

AP Calculus
The 9th term of an arithmetic progression is 4+5p and the sum of the four terms of the progression is 7p10, where p is a constant. Given that common difference of the progression is 5, find the value of p.

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

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

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

Maths
If 7 and 189 are the first and fourth terms of a geometric respectively, find the sum of the first three terms of the progression?

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.

Math
The sixth term of an arithmetic progression is 265 and the sum of the first 5 terms is 1445. Find the minimum value of n so that the sum of the first n terms is negative.

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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)

Hill school
The first three terms of a geometric progression are K3,2K4,4K3 in that order find the value of K and the sum of the first 8 terms of the progression.

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): xinfinity (1c): if An=sum r=1 to n

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

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

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

Mathematics
The sum of the geometric progression a,ar,ar^2,ar^n1 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

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

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.

Math
How do we find the sum of n terms of the following? Tr= 5^r/[(r+1)(r+2)] I can see there's an arithmetic progression and a geometric progression? How do we combine them both to find n terms.

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

Math....Please help I have a deadline for tonight!
Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.

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

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

maths
An arithmetic progression has 10 terms. Sum of the 10 terms is 220. Sum of the odd terms is 100. Find the first term and common difference. pl give me the answer.

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

math
To find three numbers in geometric progression, knowing that their sum is 78 and the highest 30 units exceeds the sum of the first and second term.

Math
An arithmetic progression has 10 terms. Sum of the 10 terms is 220. Sum of the odd terms is 100. Find the first term and common difference.

Math Algebra
The first term of a geometric progression is more than the third term by 12. The fourth term is more than the second term by 4. Find: i.the first term a and the common ratio r. ii. the n'th term of the progression.

math
In a Geometric progression the sum of its first 4 term is equal 15, and the sum of the next term is equal to 15/16. find its first term and its common ratio

math
a geometric progression is given as 8/814/27+2/9.find the sum of the first five terms.

arithmetic
an arithmetic progression has 20 terms. the sum of all the even terms is 350. given that the first term is 5, find the common difference and the eleventh term.

maths
The sum of first 6 terms of an Arithmetic progression is 6 the product of 2nd term and 5th term is 80 . Find the terms of A.P.

math
In the geometric progression, the first is a and the common ratio is r. The sun of the first two terms is 12 and the third term is 16 Determine the ratio (ar^2)/(a+ar) If the first term is larger than the second term, find the value of r.

Maths
The sum of n numbers of geometric progression is GP=(2^n+1)1. Find the first term and the common difference.

math
An arithmetic progression has 2 as its first term. find its common difference if the sum of 33 terms is equal to six times the sum of 13 terms

Math
The fifth term of an arithmetic progression is 19 and the fourteenth term is 15. Find the, first term, common difference, and sum of the first eighty terms.

Math
The second and fourth terms of Geometric progression are 9 and 4 respectively. Find the common ratio and the first term