Question

Which term of the A.P. 3, 15, 27, 39, … will be 132 more than its 54^th term?

Answer 1

a = 3, d = 15 - 3 = 12

Using T_n = a + (n - 1)d, we get

T₅₄ = a + 53d

= 3 + 53 × 12

= 3 + 636

= 639

Let Tn be 132 more than its 54^th term.

∴ T_n = T₅₄ + 132

T_n = 639 + 132

T_n = 771

a + (n - l)d = 771

3 + (n - 1) × 12 = 771

(n - 1) × 12 = 771 - 3 

(n - 1) × 12 = 768

(n - 1) = `768/12`

(n - 1) = 64

n = 64 + 1

n = 65

Thus, 132 more than 54^th term is the 65^th term.