Question

An A.P. consists of 50terms 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), weobtain

12 = a + 2 (2)

a = 12 − 4= 8

a₂₉ =a + (29 − 1) d

a₂₉ =8 + (28)2

a₂₉ =8 + 56 = 64

Therefore, 29^thterm is 64.