Question

The first term in this sequence is -1. Write the function that represents the sequence

Answer 1

`a_(n)` = 2n - 3

Explanation:

Note the difference in consecutive terms is constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2

This indicates that the terms are an arithmetic sequence with

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 2, thus

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