Answer
General Formula: $a_n=6+(n-1)(-5)$
$a_{20}=-89$
Work Step by Step
RECALL:
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:
$a_1 =6$
$d= 1 -6 = -5$
(2) Substitute the values of $a_1$ and $d$ in the general formula given above to find:
$a_n= 6+ (n-1)(-5)$
Therefore, the 20th term of the sequence is:
$a_{20} = 6 + (20-1)(-5)
\\a_{20} = 6+19(-5)
\\a_{20} = 6+ (-95)
\\a_{20} = -89$
