# Find the sum of the arithmetic sequence. -1, 2, 5, 8, 11, 14, 17

Find the sum of the arithmetic sequence. -1, 2, 5, 8, 11, 14, 17
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rougertl
An arithmetic sequence is of type $a,a+d,a+2d,a+3d,....$
in which first term is a and difference between a term and its preceding term is d.

${n}^{th}$ term of such a sequence is $a+\left(n-1\right)d$ and sum of the series up to n terms is given by $an+n\left(n-1\right)\frac{d}{2}$

In arithmetic sequence. {−1,2,5,8,11,14,17,.........}, a=−1 and d=3, hence of first n terms is $-n+\frac{3n\left(n-1\right)}{2}$, which can be simplified to $\frac{-2n+3{n}^{2}-3n}{2}$ or $\frac{3{n}^{2}-5n}{2}$

As there are 7 terms in the series, their sum is $\frac{3\cdot {7}^{2}-5\cdot 7}{3}$ or $\frac{147-35}{2}$ or $\frac{112}{2}$ or 56.