Find the nth term of the A.P. 5, 11, 17, 23,……. Using it, find its

(i) 11th term

(ii) 21st term.

Given,

a = 5

d = 11 - 5 = 6

n^th term of an A.P. is given by,

a_n = a + (n - 1)d

a_n = 5 + (n - 1)6

= 5 + 6n - 6

= 6n - 1.

(i) 11th term:

⇒ a₁₁ = 5 + (11 - 1)6

= 5 + 10(6)

= 5 + 60

= 65.

(ii) 21st term

⇒ a₂₁ = 5 + (21 - 1)6

= 5 + (20)6

= 5 + 120

= 125.

Hence, nth term = 6n - 1, 11th term = 65 and 21st term = 125.