PRACTICE PROBLEMS ON GENERAL SEQUENCE

(1)  Find the next three terms of the following sequence.

(i) 8, 24, 72, …         Solution

(ii) 5, 1,-3,…       Solution

(iii) 1/4, 2/9, 3/16,…          Solution

(2)  Find the first four terms of the sequences whose nth terms are given by

(i) a_n = n³ −2            Solution

(ii) a_n = (−1)ⁿ⁺¹ n(n + 1)       Solution

(iii) a_n = 2n² - 6       Solution

(3)  Find the nth term of the following sequences

(i) 2, 5, 10, 17,.......             Solution

(ii) 0, 1/2, 2/3, ............           Solution

(iii) 3, 8, 13, 18,...            Solution

(4)  Find the indicated terms of the sequences whose nth terms are given by

(i) a_n  =  5n / (n + 2); a₆ and a₁₃           Solution

(ii) a_n  =  -(n² - 4); a₄ and a₁₁           Solution

(5)  Find a₈ and a₁₅ whose nth term is

Solution

(6)  If a₁ = 1, a₂ = 1 and a_n = 2a_{n - 1} + a_{n - 2} n ≥ 3, n ∈ N, then find the first six terms of the sequence.

Solution

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