2(a)Consider the arithmetic progression with terms A3=2 and A12=23. Find the sum of A1+......+A40 (can do) (b)In 1800 the population of England was 8 million. The economist Malthus (17661834) produced a hypothesis, suggesting:that the population of england would increase, according
104,009 results
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

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.

AP calculus
The sixth term of an Arithmetic Progression is 23 and the sum of the six terms is 78. Find the first term and the common difference.

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.

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

math
There are two positive numbers that can be inserted between 3 and 9 such that the first three are in geometric progression while the last three are in arithmetic progression. Find the sum of those two numbers.

Mathematics
If the sixth term of an arithmetic progression is 37 and the sum of the first sixth terms is 147 find the first term

Arithmetic Progressions
The second term of an arithmetic progression I four times the fits term, and the first term is ten. Find the common difference and hence find the sum of the first 12 terms.

math
the ninth term of an arithmetic progression is 52ind the and the sum of the first twelve terms is 414.find the first term and the common difference.

arithmetic
the first and second terms of an arithmetic progression are 161 and 154 respectively.the sumthe first m terms is zero.find the value of m

arithmetic progression
An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference.

kite
the sixth term of an arithmetic progression is 21 and the sum of the first 17 terms is 0. write the first three terms.

Math
If 6, p and 14 are consecutive terms in arithmetic progression(A.P) Find the value of p

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

Maths
Pls help me out on this question, Find the sum of this first 8 terms of the Arithmetic Progression. log x, log x2, logx3

Mathematics
The 4th term of an arithmetic progression is 6.if the sum of the 8th and 9th terms is 72.what is the common difference

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

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.

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

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.

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.

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

arithmetic progression
four positive integers form an arithmetic progression . if the product of the first and the last terms is 70 and the second and third terms are 88, find the first 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

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

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

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
Given that 6,x, 4,and y are consecutive terms in an arithmetic progression, find the value of (xy)

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

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

AP calculus
Given an arithmetic progression 7,3,1,..., state three consecutive terms in this progression which sum up to 75.

arithmetic
the 20th sum of an arithmetic progression is 7 and the sum of the first 20 terms is 620. find the 1st and 30th terms i am looking at using S20 = a(1rn)/lr = 620. but i am reallys tuck and think i am very wrong. please help.

Math
2(a)Consider the arithmetic progression with terms A3=2 and A12=23. Find the sum of A1+......+A40 (can do) (b)In 1800 the population of England was 8 million. The economist Malthus (17661834) produced a hypothesis, suggesting:that the population of

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
An arithmetic progression has 11 as its first term and fourth term is 32.find the sum of the first nine terms.

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
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
The sum of the first 12terms of an arithmetic progression is 135 while the sum of the next 8 terms is 210. Find the common difference

Math
Let A1,A2...A12 be twelve equally spaced points on a circle with radius 1. Find (A1 A2)^2 + (A1 A3)^2 + ... + A11 A12)^2. (The sum includes the square of the distance between any pair of points, so the sum includes 12 choose 2 = 66 terms.)

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
I would need help with example: The three numbers are consecutive terms of arithmetic progression and the sum of their second powers is 126. The first number 3 times smaller, the second number with no change and the third number 4 times greater, are the 3

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

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!!
Three numbers are in an arithmetic progression; three other numbers are in a ge ometric progression. Adding the corresponding terms of these two progressions yields 32, 26, and 32. The sum of the three terms of the arithmetic progression is 51. Find the

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)

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
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 first and the last terms of an Arithmetic Progression are 6 and 171 in that order. If there are 14 terms, find the 16th term of the Arithmetic Progression.

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?

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

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

mathematics
if the sum of the 6th and 7th terms of an arithmetic progression is 60 and the 3rd term is 5 find the common difference

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 a particular arithmetic progression, the sum of the first 10 terms is equal to the sum of the first twenty terms. Show that the sum of the first 30 terms is equal to 0.

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

Math
The first term of an arithmetic progression is 7 and the 100th term is 502. Find the sum of the first 50 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
The third and fifth term of an arithmetic progression are 10 and10 respectively. a)Determine the first and the common difference t3 = a + 2d = 10 t5 = a + 4d = 10 a 2d = 10 a + 4d = 10 2d = 20 d = 10 a + 2(10) = 10 a 20 = 10 a = 30; d = 2 b)The

arithmetic
In an arithmetic progression the sum of the first 10 terms is 50 and the 5th is three times the second term. Find the fisrt term and the common difference.

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.

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

mathematics
if7 times the 7th terms ofan arithmetic progression is equal to 11 time is 11th terms, show that its 18th term is 0 can you find the 1st terms andthe common difference justify your answer

addmath A.P.
An arithmetic progression has 8terms.The sum of all 8terms is 180 and the sum of all odd terms is 80. Calculate (a)the first term and common difference (b)the last term

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

Calculus
An arithmetic progression has terms a8 =23 and a20 =83 . What is the value of the term a12

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

Math
A sequence is called an arithmetic progression of the rst order if the di erences of the successive terms are constant. It is called an arith metic progression of the second order if the di erences of the successive terms form an arithmetic progression of

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

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

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

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
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.

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

arithmetic
Two arithmetic progression have thd same first and last terms.the first arithmetic progression has 21 terms with a common difference of 9.How many terms has the other arithmetic progression if its common difference is 4?working and answer.thans

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.

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
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

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?

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

Trigonometry
The first three terms of an arithmetic progression are 1/2, x, 25. The first three terms of a geometric progression are x+1/4, 32 1/2, and y, where x and y are positive numbers. Find the value of X and the value of Y.

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.

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.

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.

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

AP calculus
The consecutive terms of an arithmetic progression are 5x, 8, 2x. Find the common difference of the progression.

arithmetic progression
If sum of first 21 terms of an arithmetic progression is 13 and that of first 13 terms is 21, show that sum of first 34 terms is 34 ?

arithmetic
What is the sum to 15 terms of an arithmetic progression whose 8th term is 4?

Series
2(a)Consider the arithmetic progression with terms A3=2 and A12=23. Find the sum of A1+......+A40 (can do) (b)In 1800 the population of England was 8 million. The economist Malthus (17661834) produced a hypothesis, suggesting:that the population of

series
2(a)Consider the arithmetic progression with terms A3=2 and A12=23. Find the sum of A1+......+A40 (can do) (b)In 1800 the population of England was 8 million. The economist Malthus (17661834) produced a hypothesis, suggesting:that the population of

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.

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??

Maths
In an arithmetic progression the term is 25,nth term is 17 and the sum of n terms is 132.find n and the common difference

Maths  Series
1(a)Glasses are piled upon each other to form a tower.The rows are numbered,beginning with the top row.There is a single glass in the top row,two glasses in row number 2,3 in 3;etc.This continues to the bottom of the tower.A tower is needed which uses a

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.

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. maths  Steve Monday, July 17, 2017 at 12:11pm 10/2 (2a+9d) = 220 5/2 (2a+4*2d) = 100 maths 

math
The second term of an arithmetic progression is 8 and the eleventh term is 10 Find the first term, the common differrnce and sum to 15 terms

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
Find the sum of the arithmetic progression 4 + 9 + 14 + 19 + …….94 + 99 + 104

math
Help please find three consecutive numbers, which are in arithmetic progression whose sum is 39