## Thinking Mathematically (6th Edition)

General Formula: $a_n=7+(n-1)(-4)$ $a_{20}=-69$
The formula for the general term (the nth term) of an arithmetic sequence is: $a_n=a_1 + (n-1)d$ where d = common difference $a_1$ = first term $a_n$ = nth term n = term number To find the formula for the general term, perform the following steps: (1) Find the values of $a_1$ and $d$ The given sequence has: $a_1 =7$ $d= 3 -7 = -4$ (2) Substitute the values of $a_1$ and $d$ in the general formula given above to find: $a_n= 7 + (n-1)(-4)$ Therefore, the 20th term of the sequence is: $a_{20} = 7+ (20-1)(-4) \\a_{20} = 7+19(-4) \\a_{20} = 7 + (-76) \\a_{20} = -69$