# What is the sum of the arithmetic sequence 174, 168, 162 …, if there are 37 terms?

Mar 24, 2016

Sum of the series is $2442$

#### Explanation:

Sum of an Arithmetic series

$\left\{a , \left(a + d\right) , \left(a + 2 d\right) , \ldots \left(a + \left(n - 1\right) d\right)\right\}$ up to $n$ terms is given by

$\frac{n}{2} \times \left(2 a + \left(n - 1\right) d\right)$

where $a$ is the first term and $d$ is the difference between a term and its preceding term.

Here first term $a = 174$ and $d = 168 - 174 = - 6$ and $n = 37$

Hence the desired sum is $\frac{37}{2} \times \left\{2 \times 174 + \left(37 - 1\right) \times \left(- 6\right)\right\}$ or

$\frac{37}{2} \times \left(348 - 36 \times 6\right)$ or $\frac{37}{2} \times \left(348 - 216\right)$ or

$\frac{37}{2} \times 132 = 2442$