Question

The sum of 4^th and 8^th terms of an A.P. is 24 and the sum of the 6^th and 10^th terms is 34. Find the first term and the common difference of the A.P.?

Answer 1

Given:

a₄ + a₈ = 24 …(i)

a₆ + a₁₀ = 34 …(ii)

a₄ = a + 3d

a₈ = a + 7d

a₆ = a + 5d

a₁₀ = a + 9d

Put the value of a₄ and a₈ in (i)

(a + 3d) + (a + 7d) = 24

a + 5d = 12 …(iii)

Put the value of a₆ and a₁₀ in (ii)

(a +5d) + (a +9d) = 34

a +7d = 17 …(iv)

Subtracting (iii) from (iv), we get

2d = 5

d = \(\frac{5}{2}\)

Putting the value of d in (iii), we get

a = 12 - \(\frac{25}{2}\) = \(\frac{-1}{2}\)

Hence, first term is \(\frac{-1}{2}\) and common difference is \(\frac{5}{2}\)