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

How do you find the sum of the arithmetic sequence given an = 5, d = -2, n = 12?
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Bordenauaa
We have: an=5 , d=−2 and n=12

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

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:

$Sum=\left(\frac{n}{2}\right)\left(a1+an\right)$

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

$=6×32$

$=192$

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