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

wurmiana6d 2021-11-16 Answered
To find: The sum of the given arithmetic sequence.
The sequence 2n=1802n5
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Expert Answer

oces3y
Answered 2021-11-17 Author has 21 answers

Formula used:
The formula for the summation of a polynomial with degree 1 is, k=1nk=n2(n+1)......(1)
The formula for the summation of a constantis, k=1nc=cn .....(2)
Calculation:
To find the sum of the arithmetic sequence, i.e, to find,
Sn=n=180(2n5)
Write n=1802n5 as follows,
n=1802n5=2n=180n+n=1805
Now to find 2n=180n,
Substitute the values of n in equation (1).
We get,
2n=180n
=2(80(80+1)2)
=2(80×812)
=6480
Now to find the n=1805
Substitute the values of n in equation (2).
We get,
2n=1805
=5(80)
=400
Then,
2n=180n+n=1805=6480400
=6080
Hence
n=1802n5=6080

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