Answer
First five terms are:
$a_1 = 11$
$a_2 = 18$
$a_3 = 25$
$a_4 = 32$
$a_5 = 39$
The given sequence is arithmetic with $d=7$..
The $n^{th}$ term is given by the formula:
$a_n=11+ 7(n-1)$
Work Step by Step
Find the first five terms by substituting 1, 2, 3, 4 and 5 to $n$ in the given formula.
$a_1 = 4+7(1) = 4+7=11$
$a_2 = 4+7(2) = 4+14=18$
$a_3 = 4+7(3) = 4+21=25$
$a_4 = 4+7(4) = 4+28=32$
$a_5 = 4+7(5) = 4+35=39$
A sequence is arithmetic if there exists common difference among consecutive terms. Note that the terms have a common difference of $7$.
Thus, the given sequence is arithmetic with $d=7$.
The $n^{th}$ term $a_n$ of an arithmetic sequence can be found using the formula
$a_n = a+ d(n-1)$
where
$d$ = common difference
$a$ = first term
Since the given arithmetic sequence has $a=11$ and $d=7$, then the $n^{th}$ term is given by the formula:
$a_n=11+ 7(n-1)$
