Question

The sum first 10 terms of an AP is -150 and the sum of its next 10 terms is -550 . Find the AP

Answer 1

Let a be the first term and d be the common difference of the AP. Then,

It is given that the sum of its next 10 terms is -550.

Now,

S₂₀ = Sum of first 20 terms = Sum of first 10 terms + Sum of the next 10 terms 

= -150 + (-550) = -700

∴ S₂₀ = -700

\(\Rightarrow \frac{20}{2}(2a+19d)=-700\)

\(\Rightarrow\) 10(2a + 19d) = -700

\(\Rightarrow\) 2a + 19d = -70    ......(2)

Subtracting (1) from (2), we get

Hence, the required AP is 3, -1, -5, -9,.............