# maths

A) In an arithmetic progression the sum of the first ten terms is 50 and the fifth term is three times the second term

(1) Calculate the first term
(2)Calculate the sum of the 20 terms

1. 👍
2. 👎
3. 👁
1. Just translate into Math using the definitions of AP

"the fifth term is three times the second term " ---> a+4d = 3(a+d)
a+4d = 3a+3d
d = 2a **

"the sum of the first ten terms is 50"
--> 5(2a+9d) = 50
2a+9d=10 ***

sub ** into ***
2a+9(2a) = 10
20a=10
a = 1/2
d = 1

first term is 1/2
sum(20)
= 10(2(1/2) + 19(1)) = 200

1. 👍
2. 👎

## Similar Questions

1. ### 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

2. ### 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,

3. ### 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.

4. ### Mathematics

In an arithmetic sequence the sum of the first ten terms is 400 and the sum of next ten terms is 1000. Find The common difference The first term The first three terms of arithmetic sequence are also 2x, x+4 and 2x-7. Verify that

1. ### Algebra 2

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

2. ### maths

the sum of first 8 terms of an arithmetic progression is 156.the ratio of its 12th term to its 68th term is 1:5.calculate the first term and the fifteenth term. please help this questions please.

3. ### 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.

4. ### 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.

1. ### 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.

2. ### 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

3. ### 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.

4. ### 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