Question

4^th term of an A.P. is equal to 3 times its first term and 7^th term exceeds twice the 3^rd term by 1. Find the first term and the common difference.

Answer 1

The general term of an AP is given by t_n = a + (n – 1)d

Now t₄ = 3 × a

`=>` a + 3d = 3a

`=>` 2a – 3d = 0  ...(i)

Next t₇ + 2 × t₃ = 1

`=>` a + 6d – 2(a + 2d) = 1

`=>` a + 6d – 2a – 4d = 1

`=>` – a + 2d = 1 ...(ii)

Multiplying (ii) by 2, we get

–2a + 4d = 2  ...(iii)

Adding equation (i) and (iii), we get

d = 2

Substituting the value of d in (ii), we get

–a + 2 × 2 = 1

`=>` –a + 4 = 1

`=>` a = 3

Hence a = 3 and d = 2