Question

Find:
(i) The 20th term of the AP 1, 5, 9. 13, 17,...
(ii) The 35th term of the AP 6, 9, 12, 15,...
(iii) The nth term of the AP 5, 11, 17, 23,...
(iv) The 11th term of the AP (5a − x), 6a, (7a + x),....

Answer 1

(i) The given AP is 1, 5, 9, 13, 17,...
First term, a = 1 and common difference, d = (5 - 1) = 4
T₂₀ = a + (20 - 1)d = a + 19d

= 1 + 19 ⨯ 4 = 77
∴ 20^th term = 77

(ii) T₃₅ = a + (35 - 1)d = a + 34d
= 6 + 34 ⨯ 3 = 108 [∵ a = 6 and d = 3]
∴ 35^th term = 108

(iii) T_n = a + (n - 1)d
= 5 + (n - 1) ⨯ 6
= 5 + 6n - 6 = 6n - 1 [∵ a = 5 and d = 6]
∴ n^th term = 6n - 1

(iv) T₁₁ = a + (11 - 1)d = a + 10d
= 5a - x + 10 ⨯ (a + x) [∵ a = (5a -x) and d = {6a -(5a - x)} = a + x]
= 5a - x + 10a + 10x = 15a + 9x
​ ∴ 11^th term = 15a + 9x
​