Answer
$301$
Work Step by Step
We have to determine the sum:
$S=2+5+8+.....+41$
As $5-2=8-5=...=3$, the sequence is arithmetic.
Determine its first term and the common difference:
$a_1=2$
$d=3$
The terms can be written as:
$2=3\cdot 1-1$
$5=3\cdot 2-1$
$8=3\cdot 3-1$
..............................
$41=3\cdot 14-1$
Therefore, the given sum contains $14$ terms, so we have to determine the sum of the first $14$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$2+5+8+...+41=\dfrac{14(2+41)}{2}$
$=\dfrac{14\cdot 43}{2}$
$=301$
