Question

The sum of the 3rd and the 7th term of an A.P. is 30 and the sum of the 5th and the 9th term is 56. Find the sum of the 4th and the 8th terms of the same series.
1. 46
2. 43
3. 38
4. 29

Answer 1

Correct Answer - Option 2 : 43

Concept:

The nth number in A.P. series (a_n) = a + (n-1)d

The sum of the n numbers in the series = \(\rm {n\over2}\left[2a + (n-1)d\right]\)

Where 'a' is the first number of the series and 'd' is the common difference

Calculation:

Let the first term of the A.P. be 'a' and the common difference be 'd'

Given a₃ + a₇ = 30

a + 2d + a + 6d = 30

2a + 8d = 30    ...(i)

Also given a₅ + a₉ = 56 

a + 4d + a + 8d = 56

2a + 12d = 56   ...(ii)

Adding (i) and (ii)

4a + 20d = 86

2a + 10d = 43

a + 3d + a + 7d = 43

a₄ + a₈ = 43