Answer
The fifth term is:
$a_5=1150$
Work Step by Step
RECALL:
The $n^{th}$ $a_n$ of an arithmetic sequence is given by the formula:
$a_n = a + d(n-1)$
where
$a$ = first term
$d$ = common difference
The 100th term is $-750$ and the common difference is $-20$.
Thus, $a_{100} = -750$ and the common difference is $d=-20$.
Substitute these values to the formula above to obtain:
$a_n = a + d(n-1)
\\a_{100} = a + d(100-1)
\\-750 = a + (-20)(99)
\\-750 = a + (-1980)
\\-750=a - 1980
\\-750+1980=a
\\1230=a$
This means that the $n^{th}$ term $a_n$ of the sequence is given by the formula:
$a_n=1230+(-20)(n-1)$
To solve for the fifth term, substitute $5$ to $n$ to obtain:
$a_5 =1230 + (-20)(5-1)
\\a_5=1230+(-20)(4)
\\a_5=1230+(-80)
\\a_5=1150$
