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

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 = 8

a₂₉ = a + (29 − 1) d

a₂₉ = 8 + (28)2

a₂₉ = 8 + 56 = 64

Therefore, 29^th term is 64.