Answer:
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.
