Find the first five terms of the sequence in which the nth term is given by Class 9

Find the first five terms of the sequence in which the n^th term is given by Class 9

Question 1.

Find the first five terms of the sequence in which the n^th term is given by Class 9

i. t_n = 3n - 4,

ii. t_n = 2 - 5n, and

iii. t_n = n² - 2n + 3 for n > 1.

Solution:

i. For t_n = 3n - 4,

t₁ = 3(1) - 4 = 3 - 4 = -1

t₂ = 3(2) - 4 = 6 - 4 = 2

t₃ = 3(3) - 4 = 9 - 4 = 5

t₄ = 3(4) - 4 = 12 - 4 = 8

t₅ = 3(5) - 4 = 15 - 4 = 11

∴ First five terms are -1, 2, 5, 8, 11.

ii. For t_n = 2 - 5n,

t₁ = 2 - 5(1) = 2 - 5 = -3

t₂ = 2 - 5(2) = 2 - 10 = -8

t₃ = 2 - 5(3) = 2 - 15 = -13

t₄ = 2 - 5(4) = 2 - 20 = -18

t₅ = 2 - 5(5) = 2 - 25 = -23

∴ First five terms are -3, -8, -13, -18, -23.

iii. For t_n = n² - 2n + 3,

t₁ = (1)² - 2(1) + 3 = 1 - 2 + 3 = 2

t₂ = (2)² - 2(2) + 3 = 4 - 4 + 3 = 3

t₃ = (3)² - 2(3) + 3 = 9 - 6 + 3 = 6

t₄ = (4)² - 2(4) + 3 = 16 - 8 + 3 = 11

t₅ = (5)² - 2(5) + 3 = 25 - 10 + 3 = 18

∴ First five terms are 2, 3, 6, 11, 18.