# How do you find the sum of the arithmetic sequence. -1, 2, 5, 8, 11, 14, 17?

Feb 23, 2016

#### Answer:

Just add them or use process as given below. Sum is $56$.

#### Explanation:

An arithmetic sequence is of type $a , a + d , a + 2 d , a + 3 d , \ldots .$
in which first term is $a$ and difference between a term and its preceding term is $d$.

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

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

$\frac{3 {n}^{2} - 5 n}{2}$.

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 $56$.