Question

22. For the sequence 3, 10, 17, 24, ... , write the explicit equation for this sequence, then

find the 18th term.

Answer 1

see explanation

Explanation:

Note the common difference d between consecutive terms

d = 10 - 3 = 17 - 10 = 24 - 17 = 7

This means the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

Here a₁ = 3 and d = 7, thus explicit formula is

`a_(n)` = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4, thus

`a_(18)` = (7 × 18) - 4 = 126 - 4 = 122