# How do you find the sum of the arithmetic sequence given an = 5, d = -2, n = 12?

Jun 24, 2015

 =color(blue)(192

#### Explanation:

We have: $a n = 5$ , $d = - 2$ and $n = 12$

By formula:
 color(blue)(an = a1+ (n-1)d
$5 = a 1 + \left(12 - 1\right) . \left(- 2\right)$
$5 = a 1 + 11. \left(- 2\right)$
$5 = a 1 - 22$
$a 1 = 27$

Now,
The formula for sum of an Arithmetic Sequence when the first term $a 1$, number of terms $n$ and last term $a n$ are given is:

 color(blue)(Sum = (n/2)(a1+an)

$= \frac{12}{2} \left(27 + 5\right)$

$= 6 \times 32$

 =color(blue)(192