The sum of given arithmetic sequence: sum n=1 80 2n - 5=6080

jernplate8 2021-01-19 Answered
The sum of given arithmetic sequence:
 n=1 80 2n  5=6080
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Expert Answer

Talisha
Answered 2021-01-20 Author has 93 answers
Formula used:
The formula for the summation of a polynominal with degree 1 is,  k=1 n k=n2 (n + 1) ...(1)
The formula for the summation of a constant is,  k=1 n c=cn ...(2)
Calculation:
To find the sum of the arithmetic sequence, i.e, to find,
S n= n=1 80 (2n  5)
Write  n=1 80 2n  5 as follows,
 n=1 80 2n  5=2 n=1 80 n +  n=1 80  5
Substitute the values of n in equation (1).
We get,
2  n=1 80 n
=2 (80(80 + 1)2)
=2 (80 × 81 2)
=6480
Now to find the  n=1 80  5
Substitute the values of n in equation (2).
We get,
 n=1 80  5
= 5(80)
= 400
Then,
2  n=1 80 n +  n=1 80  5=6480  400
=6080
Hence
 n=1 80 2n  5=6080.
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Jeffrey Jordon
Answered 2022-01-15 Author has 2064 answers

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