Question

In an AP. the sum of first 10 terms is 175 and the sum of the next 10terms is 475.Find the AP

Answer 1

Here is the answer.
Hope it helps!!

Answer 2

Answer:

The required AP is 4, 7, 10, 13, ...

Step-by-step explanation:

It is given that the sum of first 10 terms is 175 and the sum of the next 10 terms is 475.

Let the first term be a and the common difference be d.

The sum of an AP is

$S_n=\frac{n}{2}[2a+(n-1)d]$

The sum of 10 terms is

$S_{10}=\frac{10}{2}[2a+(10-1)d]$

$175=5[2a+9d]$

$35=2a+9d$                   .... (1)

The sum of 20 terms is

$S_20=\frac{20}{2}[2a+(20-1)d]$

$175+475=10[2a+19d]$

$65=2a+19d$                   .... (2)

On solving (1) and (2) we get

$a=4, d=3$

The AP is

$4,4+3,4+2(3)+4+3(3)+...$

$4, 7, 10, 13...$