Question

in an ap , sum of first ten term is -150 and the sum of its next ten terms is -550 .find the ap​

Answer 1

Given : Sum of first ten term = -150

Sum of it's next ten terms = -550

To find = AP

Solution :

The sum of the first n terms of an AP isSn = (n/2)[2a + (n-1)·d]n = 10, S10 = -150-150 = (10/2)[2a + (10 - 1)d]-150 = 5[2a + 9d]

Dividing through by 5,

Dividing through by 5,-30 = 2a + 9d ----------(1)

Given sum ofits next 10 terms is - 550.

Given sum ofits next 10 terms is - 550.n = 10, Sn = - 550Here a = a + 10d- 550 = (10/2)[2(a + 10d) + (10-1)d]- 550 = 5[2a + 29d]Dividing through by 10,

-110 = 2a + 29d ----------(2)

-110 = 2a + 29d ----------(2)Solving (1) and (2) we get

d = -4 and a = 3.

And we are done!

AP = 3,-1,-5 ... (◕ᴗ◕✿)