Question

In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.

Answer 1

Here, we are given and sum of the next ten terms is −550.

Let us take the first term of the A.P. as a and the common difference as d.

So, let us first find a₁₀. For the sum of first 10 terms of this A.P,

First term = a

Last term = a₁₀

So, we know,

For the 10^th term (n = 10),

So, here we can find the sum of the n terms of the given A.P., using the formula,

Where, a = the first term

l = the last term

So, for the given A.P,

Similarly, for the sum of next 10 terms (S₁₀),

First term = a₁₁

Last term = a₂₀

For the 11^th term (n = 11),

For the 20^th term (n = 20),

So, for the given A.P,

Now, subtracting (1) from (2),

Substituting the value of d in (1)

So, the A.P. is with .