Question

Fourth term of an A.P is 16 and 9th term of same A.P 36. Find the sum of its 15th term. Select one: a. 126 b. 122 c. None of these d. 130

Answer 1

Given: Fourth term of an AP is 16 and 9th term of same AP is 36

To find: Sum of its first 15 terms

Solution:

We know that nth term of an AP is given by,

an = a + (n - 1)d

Using this formula, we get the following results:

16 = a + 3d  _____________(1)

36 = a + 8d ______________(2)

Now subtract equation (2) from (1)

=> 36 - 16 = a + 8d - a - 3d

=> 20 = 5d

=> 4 = d

Substitute this value in equation (1)

=> 16 = a + 3(4)

=> 16 = a + 12

=> 16 - 12 = a

=> 4 = a

Now to find the sum of n terms, we have formula:

⇒ Sn = n/2 [2a + (n - 1)d]

⇒ S15 = 15/2 [2(4) + (15 - 1)4]

⇒ S15 = 15/2[8 + 14(4)]

⇒ S15 = 15/2[8 + 56]

⇒ S15 = 15/2[64]

⇒ S15 = 15*32

⇒ S15 = 480

Hence the sum of 15 terms is 480.

Answer is [C] none of these.