Find the sum of the first n terms of the following arithmetic sequence: Second term is 13, third term is 21; n = 17
A) 1,219
B) 1,173
C) 1,085
D) 1,112

Question

Quizplus · Accepted Answer

The common difference can be found by subtracting the third term from the second term: 
$d = 21-13= 8$
The formula for the sum of an arithmetic series is: 
$S_n = \frac{n}{2}(a_1+a_n)$
where $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms.

We know that $a_2 = 13$ and $d = 8$, so we can find $a_1$: 
$a_1 = a_2 - d = 13-8 = 5$

Then we can find $a_{17}$: 
$a_{17} = a_1 + (n-1)d = 5 + (17-1)8 = 133$

Finally, we can substitute into the formula for $S_{17}$:

$S_{17} = \frac{17}{2}(5+133) = 1173$

Therefore, the answer is B.

Find the Sum of the First N Terms of the Following