Find the 10th and 15th terms of the sequence tn = 5n - 3 for n ≥ 1. Class 9

Find the 10^th and 15^th terms of the sequence t_n = 5n - 3 for n ≥ 1. Class 9

Question 1.

Find the 10^th and 15^th terms of the sequence t_n = 5n - 3 for n ≥ 1. Class 9

Solution:

Given, t_n = 5n - 3 for n ≥ 1

For n = 10,

t₁₀ = 5(10) - 3 = 50 - 3 = 47

For n = 15,

t₁₅ = 5(15) - 3 = 75 - 3 = 72

The 10^th and 15^th term of the sequence is 47 and 72, respectively.

Question 2.

Determine whether 97 and 172 are terms of the sequence t_n = 5n - 3 for n ≥ 1. Class 9

Solution:

Given, t_n = 5n - 3 for n ≥ 1

i. Let t_n = 97

∴ 5n - 3 = 97

∴ 5n = 100

n = $\frac{100}{5}$

∴ n = 20

Since n is a natural number,

∴ 97 is a term of the sequence.

ii. Let t_n = 172

∴ 5n - 3 = 172

∴ 5n = 175

∴ n = 35

Since n is a natural number,

∴ 172 is a term of the sequence.