Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 89, 178, 267, 356, ...

a (n) = 89n

Step-by-step explanation:

Given the sequence 89, 178, 267, 356, ...

First Term, a (1) = 89

178-89=267-178=89

This is an arithmetic difference with:

Common difference, d=89

The position of any term, n in an arithmetic sequence is derived using the formula:

a (n) = a (1) + (n-1) d

Substituting a (1) = 89 and d=89

a (n) = 89+89 (n-1)

a (n) = 89+89n-89

a (n) = 89n

The expression that describes the sequence above is: a (n) = 89n where n is the position of a term in the sequence.