Answer
$324$
Work Step by Step
We have to determine the sum:
$S=5+9+13+.....+49$
As $9-5=13-9=...=4$, the sequence is arithmetic.
Determine its first term and the common difference:
$a_1=5$
$d=4$
The terms can be written as:
$5=4\cdot 1+1$
$9=4\cdot 2+1$
$13=4\cdot 3+1$
..............................
$49=4\cdot 12+1$
Therefore, the given sum contains $12$ terms, so we have to determine the sum of the first $12$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$5+9+13+...+49=\dfrac{12(5+49)}{2}$
$=\dfrac{12\cdot 54}{2}$
$=324$
