Given the arithmetic sequence defined by the recurrence relation $$a_n=a_{n−1}+5$$ where $$a_1=2$$ and $$ n1$$, find an equation that gives the general term in terms of $$a_1$$ and the common difference $$d$$

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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 $$d$$

Uniteasy Admin · Accepted Answer

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,
$$a_n=a_1+(n-1)d$$
$$a_n=2+5(n-1)=5n-3$$

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