Find the sum of a given arithmetic sequence: sum n=1 100 (6 - 12 n)

allhvasstH 2021-01-27 Answered
Find the sum of a given arithmetic sequence:
 n=1 100 (6  12 n)
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Expert Answer

d2saint0
Answered 2021-01-28 Author has 89 answers
Formula used:
a)  k=1 nk=n 2 (n + 1)
b)  k=1 n c=cn
Calculation:
In order to find the sum of an arithmetic sequence, you need
S n= n=1 100 (6  12n)
Write  n=1 100 (6  12n) as follows,
 n=1 100 (6  12n)= n=1 100 6  12  n=1 100 n
Now to find  n=1 100 6,
Substitute the values of n in equation (b).
We get,
 n=1 100 6
=6 (100)
=600
Now to find the 12  n=1 100 n
Substitute the values of n in equation (a).
We get,
12  n=1 100 n
=12 (100(100 + 1)2)
=(100 × 101 4)
=2525
Then,
 n=1 100 6  12  n=1 100 n=600  2525
= 1925
Hence
 n=1 100(6  12n) = 1925
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Jeffrey Jordon
Answered 2022-01-15 Author has 2262 answers

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