Question

If the sum of 1st n terms in an AP is -150and the sum of next 10 terms is-550. Than find the AP

Answer 1

Answer:

AP = 3 , -1 , -5 , -9 ...

Step-by-step explanation:

Given: Sum of 1st 10 terms of an AP is -150

           Sum of next 10 terms is -550.

To find: AP

let the first term of an AP is a, and common difference is d.

We formula of sum of n terms,

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

⇒  $S_{10}=\frac{10}{2}(2a+(10–1)d)$

     $-150=5(2a+9d)$

      -30 = 2a + 9d

      2a = -30 – 9d ..........…(1)

$S_{20}=\frac{20}{2}(2a+(20–1)d)$

$-550+(-150)=10(2a+19d)$

$-700=10(2a+19d)$

      -70 = 2a + 19d

       2a = -70 – 19d .......…(2)

Equate (1) and (2)

-30 – 9d = -70 – 19d

10d  = -40

d = -4

From (1)

2a = -30 + 36

2a = 6

a = 3

Therefore, 1st Term is 3 and common difference is -4 ⇒ AP = 3 , -1 , -5 , -9 ...

Answer 2

Hope this may help u guys