Answer
Formula for the general term (the $n^{th}$ term) = $a_{1}$ + (n-1)d = 2n + 1
Work Step by Step
Given
$3^{rd}$ term $a_{3}$ = $a_{1}$ + (3-1)d = $a_{1}$ + 2 d = 7.
$8^{th}$ term $a_{8}$ = $a_{1}$ + (8-1)d = $a_{1}$ + 7 d = 17.
where d = common difference in sequence
On subtract $a_{3}$ from $a_{8}$.
$a_{1}$ + 7 d - $a_{1}$ - 2 d = 17 - 7
5 d = 10
d = 2
put the value of d in $a_{3}$ we got $a_{1}$ = 3.
Now the sequence will be = 3, 5, 7, 9, 11, 13, 15, 17, . . . .
Formula for the general term (the $n^{th}$ term) = $a_{1}$ + (n-1)d = 3 + (n - 1) 2 = 3 + 2n - 2 = 1 + 2n
