Question

In an AP the sum of first 10 terms is -80 and the sum of next 10 yerms is -280.
Find the AP.

Answer 1

It will Help U

$have \: a \: great \: day$

Answer 2

The required A. P is 1 , -1 , -3 , -5 , ...... , so on.

Explanation:

Sum of first n terms in A.P.= $S_n=\dfrac{n}{2}(2a+(n-1)d)$ , where a= first term ad d= common difference.

Let our required AP is a , a+d , a+2d , a+3d , ..... so on.

Given : AP the sum of first 10 terms is -80.

i.e. $S_{10}= \dfrac{10}{2}(2a+(10-1)d)=-80$

$2a+9d= -16$                     (1)

The sum of next 10 terms is -280.

Then, the sum of first 20 terms together = -80+(-280) =-360

$S_{20}=\dfrac{20}{2}(2a+(20-1)d)=-360$

$2a+19d=-36$                       (2)

Subtract (1) from (2) , we get

$10d= -20\Rightarrow\ d=-2$

Put this in (1) , we get

$2a+9(-2)=-16\Rightarrow\ 2a= -16+18\\\\\Rightarrow\ a=1$

Our required A. P will be :

1 , 1+(-2) , 1+2(-2) , 1+3(-2) , ....... so on.

1 , -1 , -3 , -5 , ...... , so on.

# Learn more :

Nth term of an AP is An=3+4n.Find the AP.

https://brainly.in/question/1868440