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

Question

Find the sum of a given arithmetic sequence:

\sum n = 1 100 (6 - 12 n)

Answer 1

Formula used:
a)

\sum k = 1 n k = n 2 (n + 1)

b)

\sum k = 1 n c = c n

Calculation:
In order to find the sum of an arithmetic sequence, you need

S n = \sum n = 1 100 (6 - 12 n)

Write

\sum n = 1 100 (6 - 12 n)

as follows,

\sum n = 1 100 (6 - 12 n) = \sum n = 1 100 6 - 12 \sum n = 1 100 n

Now to find

\sum n = 1 100 6,

Substitute the values of n in equation (b).
We get,

\sum n = 1 100 6

= 6 (100)

= 600

Now to find the

12 \sum n = 1 100 n

Substitute the values of n in equation (a).
We get,

12 \sum n = 1 100 n

= 12 (100 (100 + 1) 2)

= (100 \times 101 4)

= 2525

Then,

\sum n = 1 100 6 - 12 \sum n = 1 100 n = 600 - 2525

= - 1925

Hence

\sum n = 1 100 (6 - 12 n) = - 1925

Answer 2

Jeffrey Jordon

Answered 2022-01-15 Author has 2262 answers

Answer is given below (on video)

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