Answer
Hence, the error is in the last step. The correct $n^{nt}$ term of the arithmetic sequence is $a_n=8n+6$.
Work Step by Step
The given arithmetic sequence is
$14,22,30,38,...$
The first term $a_1=14,$
and the common difference is $d=22-14=8$
The $n^{th}$ term formula is
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $14$ for $a_1$ and $1$ for $8$.
$\Rightarrow a_n=14+(n-1)8$
Simplify.
$\Rightarrow a_n=14+8n-8$
$\Rightarrow a_n=8n+6$
Hence, the error is in the last step. The correct $n^{nt}$ term of the arithmetic sequence is $a_n=8n+6$.
