Question

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, ...

Answer 1

a(n)=89n

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.