Question

Write the explicit rule,

Answer 1

`a_(n)` = 20n + 12

Explanation:

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

d = 52 - 32 = 72 - 52 = 92 - 72 = 20

This indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 32 and d = 20, thus

`a_(n)` = 32 + 20(n - 1) = 32 + 20n - 20 = 20n + 12