Question

The first four numbers in a pattern are shown below.

3, 8, 13, 18, ...
If the pattern continues,
which expression can be used to find the nth number in the pattern?

Answer 1

`a_(n)` = 5n - 2

Explanation:

The terms have a common difference between consecutive terms, that is

8 - 3 = 13 - 8 = 18 - 13 = 5

This means the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference, thus

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