Question

If the sum of first 8 terms of an arithmetic progression is 136 and that of first 15 terms is 465 then find the sum of first 25 terms

Answer 1

Step-by-step explanation:

See the above pictures.

Answer 2

The sum of first 25 terms is 1275.

Explanation:

In an A.P. the sum of first n terms is given by :-

$S_n=\dfrac{n}{2}(2a+(n-1)d)$

, where a= first term

d= common difference

As per given , we have

$\dfrac{8}{2}(2a+(8-1)d)=136\\\\ 2a+7d=34--------(1)$

$\dfrac{15}{2}(2a+(15-1)d)=465\\\\ 2a+14d=\dfrac{465\times2}{15}\\\\2a+14d= 62--------(2)$

Subtract equation(1) from (2) , we get

$7d=28\\\\ d=4$

Put value of d=4 in (1) , we get

$2a+7(4)=34\\\ 2a=6\\\\ a=3$

Now , sum of first 25 terms will be :

$S_{25}=\dfrac{25}{2}(2(3)+24(4))=1275$

Hence, the sum of first 25 terms is 1275.

# Learn more :

The sum of the first 15 terms of an arithmetic progression is 105 and the sum of the next 15 terms is 780. Find the first three terms of the arithmetic progression.

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