Question

2) Write an equation that
describes the sequence:
2, 7, 12, 17. Find the 24th term.

Answer 1

see explanation

Explanation:

There is a common difference d between consecutive terms, that is

d = 7 - 2 = 12 - 7 = 17 - 12 = 5

This indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 5 , then

`a_(n)` = 2 + 5(n - 1) = 2 + 5n - 5 = 5n - 3

Then

a₂₄ = 5(24) - 3 = 120 - 3 = 117