Answer
$a_n=7-4(n-1)$;
$a_{20} = -69$
Work Step by Step
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:
$d =3-7
\\d = -4$
The given arithmetic sequence has $a_1=7$ and $d=-4$.
Substitute these values into the formula in (1) above to obtain the arithmetic sequence's formula for the general term:
$a_n=7+(-4)(n-1)
\\a_n=7-4(n-1)$
Solve for the 20th term for the sequence using the formula above to obtain:
$a_{20} = 7 - 4(20-1)
\\a_{20} = 7-4(19)
\\a_{20} = 7-76
\\a_{20} = -69$
