The 4 th term of an AP is three times the first and the 7 th term exceeds twice the third term by 1. Find the first term and the common difference.

Question

Philoid · Accepted Answer

To Find: First term (a) and common difference (d)

Given: a₄= 3a₁ and a₇ = 2a₃ + 1

(Where a=a₁ is first term, a_n is nth term and d is common difference of given AP)

Formula Used: a_n = a + (n - 1)d

a₄= 3a₁ a + 3d= 3a 3d = 2a ….equation (i) and

a₇ = 2a₃ + 1 a + 6d= 2(a + 2d) + 1 2d= a + 1 ….equation (ii)

on solving both equation (i) & (ii), we get

a= 3 and d= 2

So the first term is equal to 3, and the common difference is equal to 2.