Answer
$324$
Work Step by Step
The nth term of an arithmetic sequence is given by: $a_n=a_1+(n-1) d \\ 49=5+4(n-1) \\11 =n-1 \\ n=12$
We see that there is a constant difference between the terms of $d=4$ and the terms are part of an arithmetic sequence.
The terms of the sum are the first $12$ terms of the arithmetic sequence, starting with $a_{1}=5$ and with a difference of $d=4$
The sum is thus given as:
$S_{n}= \dfrac{n}{2}\left(a_{1}+a_{n}\right)$
Now, $S_{12}= \dfrac{12}{2}[5+59] \\=(6)(54) \\=324$
Therefore, the sum of the arithmetic sequence is: $324$.
