# Find the sum of the arithmetic series 2 + 5 + 8 + ... + 53

Find the sum of the arithmetic series 2 + 5 + 8 + ... + 53
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Anabelle Hicks
${t}_{n}=a+\left(n-1\right)d$
$53=2+\left(n-1\right)3$
$53=2+3n-3$
$54=3n$
$18=n$
Now that we know the number of terms we can use the formula ${s}_{n}=\frac{n}{2}\left({t}_{1}+{t}_{n}\right)$
${s}_{18}=\frac{18}{2}\left(2+53\right)$
${s}_{18}=9\left(55\right)$
${s}_{18}=495$
The sum is of 495.
When finding the sum of an arithmetic series, there are two formulas that you may use: the one presented above and ${s}_{n}=\frac{n}{2}\left\{2a+\left(n-1\right)d\right\}$. You use the latter when you don't know the last term.