A sequence is given by the recursive rule t1 = - 5, tn+1 = tn + 3 for n ≥ 1.

A sequence is given by the recursive rule t₁ = - 5, t_n+1 = t_n + 3 for n ≥ 1.

Question 1.

A sequence is given by the recursive rule t₁ = - 5, t_n+1 = t_n + 3 for n ≥ 1. Find the first five terms of the sequence. Is 52 a term of this sequence? If so, which term is it? Class 9

Solution:

i. Given, t₁ =-5, t_n+1 = t_n + 3 for n ≥ 1

t₂ = t₁ + 3 = -5 + 3 = -2

t₃ = t₂ + 3 = -2 + 3 = 1

t₄ = t₃ + 3 = 1 + 3 = 4

t₅ = t₄ + 3 = 4 + 3 = 7

∴ First five terms are -5, -2, 1, 4, 7 .

ii. Since each term of the sequence is obtained S by adding 3 to the previous term.

∴ t₂ = -5 + 3 = -5 + 3(2 - 1)

∴ t₃ = -2 + 3 = -5 + 3(3 - 1)

∴ t₄ = 1 + 3 = -5 + 3(4 - 1)

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∴ t_n = - 5 + 3 (n -1) is the explicit rule for n^th term of the sequence.

Let t_n = 52

∴ 52 = - 5 + 3 (n - 1)

∴ 52 + 5 = 3 (n - 1)

∴ 57 = 3 (n -1)

∴ $\frac{57}{3}$ = n - 1

∴ n - 1 = 19

∴ n = 20

Since n is a natural number,

∴ 52 is the 20^th term of the sequence.