Question

Use the formula an = d (n − 1) + aj to write a formula for the arithmetic sequence below.

2, 6, 10, 14, 18,

Answer 1

`a_(n)` = 4n - 2

Explanation:

There is a common difference d between consecutive terms in the sequence, that is

6 - 2 = 10 - 6 = 14 - 10 = 18 - 14 = 4

This indicates 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

Here a₁ = 2 and d = 4 , thus

`a_(n)` = 2 + 4(n - 1) = 2 + 4n - 4 = 4n - 2