Question

What is the general term of the arithmetic sequence – 32, – 25, –18, –11, …?

Answer 1

`a_1=-32\\a_2=-32+7=-25\\a_3=-25+7=-18\\a_4=-18+7=-11\\\vdots\\\\\text{The general term of an arithmetic sequence}\ a_n=a_1+(n-1)d\\\\a_1=-32,\ d=7\\\\\text{Substitute}\\\\a_n=-32+(n-1)(7)\qquad\text{use distributive property}\\\\a_n=-32+(n)(7)+(-1)(7)\\\\a_n=-32+7n-7\\\\\boxed{a_n=7n-39}`