Question

In an A.P, the sum of its first ten terms is -80 and sum of its next 10 terms is -280.

Find the A.P.

Answer 1

hey dear,

refer to given attachment please.

use the given formula:-

Sn = n/2 [2a + (n - 1 )d]

Answer 2

Answer:

The AP series is 1,-1,-3,-5....

Step-by-step explanation:

Given : In an A.P, the sum of its first ten terms is -80 and sum of its next 10 terms is -280.

To find : The A.P

Solution :

A.P series is a+a+d,a+2d,......

a is the first term , d is the common difference

The formula of sum of n terms is

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

Where n is the number of terms

The sum of its first ten terms is -80

$-80=\frac{10}{2}[2a+(10-1)d]$

$-80=5[2a+9d]$

$-16=2a+9d$......[1]

Sum of its next 10 terms is -280.

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

$S_{20}=10[2a+19d]$  

We know,

$S_{20}-S_{10]=-280$  

$10[2a+19d]-(-80)=-280$  

$10[2a+19d]=360$  

$2a+19d=-36$  ........[2]

Subtract [1] from [2]

$2a+19d-2a-9d=-36+16$

$10d=-20$

$d=-2$

Put value of d in [1]

$-16=2a+9d$

$-16=2a+9(-2)$

$-16=2a-18$

$2=2a$

$a=1$

Therefore, The AP series is 1,-1,-3,-5....