Question

The first term as well as the common difference of the second AP each is one more than the 1^st term and the common difference of the 1^st AP. The fourth term of the second AP is 15 and 5^th term of the 1^st AP is 13. Find the average of the second terms of both the AP.
1. 5
2. 4
3. 3
4. 8

Answer 1

Correct Answer - Option 4 : 8

Given:

The first term as well as the common difference of the second AP each is one more than the 1^st term and the common difference of the 1^st AP. The fourth term of the second AP is 15 and 5^th term of the 1^st AP is 13.

Formula used:

nth term of an AP, T_n = a + (n - 1)d, where ‘a’ is the first term, ‘n’ is the total number of terms and ‘d’ is the common difference.

Calculation:

Let the first term and common difference of the first AP is a1 and d1 respectively.

Let the first term and common difference of the second AP is a2 and d2 respectively.

From the question

a2 – a1 = 1     ----(1)

d2 – d1 = 1     ----(2)

Fourth term of second AP = a2 + 3d2 = 15      ----(3)

Fifth term of first AP = a1 + 4d1 = 13      ----(4)

From equation (1) (2) and (3) by putting values we get,

a1 + 1 + 3(d1 + 1) = 15

⇒ a1 + 3d1 = 11      ----(5)

Subtract equation (5) from (4)

d1 = 2

And a1 = 5

By putting the value of a1 and d1 in equation (1) and (2) we get,

a2 = 6 and d2 = 3

Second term of first AP = a1 + d1 = 7

Second term of second AP = a2 + d2 = 9

Average of both the terms = (9 + 7)/2 = 8

Thus the correct answer is 8.