## Intermediate Algebra for College Students (7th Edition)

$a_n=-20-4(n-1)$; $a_{20} = -96$
RECALL: (1) The $n^{th}$ term, $a_n$, of an arithmetic sequence can be found using the formula: $a_n=a_1 + d(n-1)$ where $a_1$ = first term $n$ = term number $d$ = common difference (2) The common difference $d$ can be determined using the formula $d= a_n-a_{n-1}$ where $a_n$ = $n^{th}$ term $a_{n-1}$ = term before $a_n$ Solve for the common difference using formula (2) above to obtain: $d =-24-(-20) \\d = -24+20 \\d=-4$ The given arithmetic sequence has $a_1=-20$ and $d=-4$. Substitute these values into the formula in (1) above to obtain the arithmetic sequence's formula for the general term: $a_n=-20+(-4)(n-1) \\a_n=-20-4(n-1)$ Solve for the 20th term for the sequence using the formula above to obtain: $a_{20} = -20 - 4(20-1) \\a_{20} = -20-4(19) \\a_{20} = -20-76 \\a_{20} = -96$