Question

The first four terms of a sequence are, 9,2,-5,-12.

State the pattern of the sequence using algebraic expressions.

Answer 1

`a_(n)` = 16 - 7n

Explanation:

There is a common difference between consecutive terms , that is

2 - 9 = - 5 - 2 = - 12 - (- 5) = - 7

This indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 9 and d = - 7 , then

`a_(n)` = 9 - 7(n - 1) = 9 - 7n + 7 = 16 - 7n