Question

If 12th term of the ap is -13 and sum of its first four term is 24. what is sum of first ten terms?

Answer 1

We know that nth term of an AP an = a + (n - 1) * d.

(i)

Given : 12th term of the AP is -13.

⇒ a12 = a + (12 - 1) * d

⇒ -13 = a + 11d      ----- (1)

(ii)

We know that Sum of first n terms of an AP is sn = n/2[2a + (n - 1) * d]

Given : sum of its first four term is 24.

⇒ s4 = (4/2)[2a + (4 - 1) * d]

⇒ 24 = 2[2a + 3d]

⇒ 12 = 2a + 3d     ------ (2)

On solving (1) * 2 & (2) , we get

⇒ 2a + 22d = -26

⇒ 2a + 3d = 12

   ---------------------

            19d = -38

                d = -2

Substitute d = -2 in (2), we get

⇒ 12 = 2a + 3d

⇒ 12 = 2a + 3(-2)

⇒ 12 = 2a - 6

⇒ 18 = 2a

⇒ a = 9

Now,

Sum of first tern terms:

⇒ n/2[2a + (n - 1) * d]

⇒ 10/2[2(9) + (10 - 1) * (-2)]

⇒ 5[18 - 18]

⇒ 0.

Therefore, Sum of first ten terms = 0.

Hope this helps!