Answer
Formula for the general term (the $n^{th}$ term) = $a_{1}$ + (n-1)d = 3n - 2
Work Step by Step
Given
$2^{nd}$ term $a_{2}$ = $a_{1}$ + (2-1)d = $a_{1}$ + d = 4.
$6^{th}$ term $a_{6}$ = $a_{1}$ + (6-1)d = $a_{1}$ + 5d = 16.
where d = common difference in sequence
On subtract $a_{2}$ from $a_{6}$.
$a_{1}$ + 5d - $a_{1}$ - d = 16 - 4
4d = 12
d = 3
put the value of d in $a_{2}$ we got $a_{1}$ = 1.
Now the sequence will be = 1, 4, 7, 10, 13, 16, . . . .
Formula for the general term (the $n^{th}$ term) = $a_{1}$ + (n-1)d = 1 + (n - 1) 3 = 1 + 3n - 3 = 3n - 2
