Find:
(i) The 10th term of the AP 63, 58, 53, 48,...
(ii) The 14th term of the AP 9, 5, 1, −3,...
(iii) The nth term of the AP 16, 9, 2, −5,...

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Solution

(i) The given AP is 63, 58, 53,48,...
First term, a = 63 and common difference, d = (58 - 63) = -5
T₁₀= a + (10 - 1)d = a + 9d
= 63 + 9 ⨯ (-5) = 63 - 45 = 18
∴ 10^th term = 18

(ii) T₁₄ = a + (14 - 1)d = a + 13d
= 9 + 13 ⨯ (-4) = 9 - 52 = -43 [∵ a = 9 and d = - 4]
∴ 14^th term = - 43

(iii) T_n = a + (n - 1)d
= 16 + (n - 1) ⨯ (-7) [∵ a = 16 and d = - 7]
= 16 - 7n + 7 = 23 - 7n
∴ n^th term = 23 -7n

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