# To find: The sum of the given arithmetic sequence. The sequence

To find: The sum of the given arithmetic sequence.
The sequence $2\sum n=1802n-5$
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Formula used:
The formula for the summation of a polynomial with degree 1 is, $\sum k=1nk=n2\left(n+1\right)$......(1)
The formula for the summation of a constantis, $\sum k=1nc=cn$ .....(2)
Calculation:
To find the sum of the arithmetic sequence, i.e, to find,
$Sn=\sum n=180\left(2n-5\right)$
Write $\sum n=1802n-5$ as follows,
$\sum n=1802n-5=2\sum n=180n+\sum n=180-5$
Now to find $2\sum n=180n$,
Substitute the values of n in equation (1).
We get,
$2\sum n=180n$
$=2\left(80\left(80+1\right)2\right)$
$=2\left(80×812\right)$
$=6480$
Now to find the $\sum n=180-5$
Substitute the values of n in equation (2).
We get,
$2\sum n=180-5$
$=-5\left(80\right)$
$=-400$
Then,
$2\sum n=180n+\sum n=180-5=6480-400$
$=6080$
Hence
$\sum n=1802n-5=6080$