Question

An A.P. consists of 50 terms of which 3^rd term is 12 and the last term is 106. Find the 29^th term of the A.P.

Answer 1

Given that,

a₃ = 12

a₅₀ = 106

We know that,

a_n = a + (n − 1)d

a₃ = a + (3 − 1)d

12 = a + 2d             ...(i)

Similarly, a₅₀ = a + (50 − 1)d

106 = a + 49d        ...(ii)

On subtracting (i) from (ii), we obtain

94 = 47d

d = 2

From equation (i), we obtain

12 = a + 2(2)

a = 12 − 4

a = 8

a₂₉ = a + (29 − 1)d

a₂₉ = 8 + (28)2

a₂₉ = 8 + 56

a₂₉ = 64

Therefore, 29^th term is 64.