Find the sum of a given arithmetic sequence:

$\sum \text{}n=1\text{}100\text{}(6\text{}-\text{}12\text{}n)$

allhvasstH
2021-01-27
Answered

Find the sum of a given arithmetic sequence:

$\sum \text{}n=1\text{}100\text{}(6\text{}-\text{}12\text{}n)$

You can still ask an expert for help

d2saint0

Answered 2021-01-28
Author has **89** answers

Formula used:

a)$\sum \text{}k=1\text{}nk=n\text{}2\text{}(n\text{}+\text{}1)$

b)$\sum \text{}k=1\text{}n\text{}c=cn$

Calculation:

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

$S\text{}n=\sum \text{}n=1\text{}100\text{}(6\text{}-\text{}12n)$

Write$\sum \text{}n=1\text{}100\text{}(6\text{}-\text{}12n)$ as follows,

$\sum \text{}n=1\text{}100\text{}(6\text{}-\text{}12n)=\sum \text{}n=1\text{}100\text{}6\text{}-\text{}12\text{}\sum \text{}n=1\text{}100\text{}n$

Now to find$\sum \text{}n=1\text{}100\text{}6,$

Substitute the values of n in equation (b).

We get,

$\sum \text{}n=1\text{}100\text{}6$

$=6\text{}\left(100\right)$

$=600$

Now to find the$12\text{}\sum \text{}n=1\text{}100\text{}n$

Substitute the values of n in equation (a).

We get,

$12\text{}\sum \text{}n=1\text{}100\text{}n$

$=12\text{}\left(100(100\text{}+\text{}1)2\right)$

$=(100\text{}\times \text{}101\text{}4)$

$=2525$

Then,

$\sum \text{}n=1\text{}100\text{}6\text{}-\text{}12\text{}\sum \text{}n=1\text{}100\text{}n=600\text{}-\text{}2525$

$=\text{}-1925$

Hence

$\sum \text{}n=1\text{}100(6\text{}-\text{}12n)\text{}=\text{}-1925$

a)

b)

Calculation:

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

Write

Now to find

Substitute the values of n in equation (b).

We get,

Now to find the

Substitute the values of n in equation (a).

We get,

Then,

Hence

Jeffrey Jordon

Answered 2022-01-15
Author has **2262** answers

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