Find the nth term of the A.P. 13, 7, 1, -5, -11, ……. Using it, find its

(i) 9th term

(ii) 16th term.

Given,

a = 13

d = 7 - 13 = -6

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

a_n = a + (n - 1)d

a_n = 13 + (n - 1)(-6)

= 13 - 6n + 6

= 19 - 6n.

(i) 9th term

⇒ a₉ = 13 + (9 - 1).(-6)

= 13 + 8(-6)

= 13 - 48

= -35.

(ii) 16th term

⇒ a₁₆ = 13 + (16 - 1).(-6)

= 13 + (15).(-6)

= 13 - 90

= -77.

Hence, nth term = 19 - 6n, 9th term = -35 and 16th term = -77.