#### Question

Given the arithmetic sequence defined by the recurrence relation a_n=a_{n−1}+5 where a_1=2 and n>1, find an equation that gives the general term in terms of a_1 and the common difference d

Question

Based on the recurrence relation a_n=a_{n−1}+5,

a_n-a_{n−1}=5

The series is an arithmetic sequence where a_1=2 and the common difference is 5.

Using the formula for general terms of an arithmetic sequence,

a_n=a_1+(n-1)d

a_n=2+5(n-1)=5n-3