Answer
$a_n=-\frac{1}{3} + \frac{1}{3}(n-1)$;
$a_{20} = 6$
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 $a_n$
The given arithmetic sequence has $a_1=-\frac{1}{3}$ and $d=\frac{1}{3}$.
Substitute these values into the formula in (1) above to obtain the arithmetic sequence's formula for the general term:
$a_n=-\frac{1}{3}+(\frac{1}{3})(n-1)$
Solve for the 20th term for the sequence using the formula above to obtain:
$a_{20} = -\frac{1}{3} + \frac{1}{3}(20-1)
\\a_{20} = -\frac{1}{3}+\frac{1}{3}(19)
\\a_{20} = -\frac{1}{3}+\frac{19}{3}
\\a_{20} = \frac{18}{3}
\\a+{20} = 6$
