Answer
General Formula: $a_n=7+(n-1)(-4)$
$a_{20}=-69$
Work Step by Step
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:
$a_{20} = 7+ (20-1)(-4)
\\a_{20} = 7+19(-4)
\\a_{20} = 7 + (-76)
\\a_{20} = -69$
