Question

Evaluate the summation of 3 times negative 2 to the n minus 1 power, from n equals 1 to 5..

Answer 1

Answer: 33

Explanation:

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Answer 2

`\sum_(n=1)^53(-2)^(n-1) = 33`

EXPLANATION

The given series is

`\sum_(n=1)^53(-2)^(n-1)`

This is a geometric series with general term,

`a_n=3( { - 2)}^(n - 1)`

The terms are:

`a_1=3( { - 2)}^(1- 1) = 3`

`a_2=3( { - 2)}^(2- 1) = - 6`

`a_3=3( { - 2)}^(3- 1) = 12`

`a_4=3( { - 2)}^(4 - 1) = - 24`

`a_5=3( { - 2)}^(5- 1) = 48`

This implies that,

`\sum_(n=1)^53(-2)^(n-1) = 3 + - 6 + 12 + - 24 + 48`

`\sum_(n=1)^53(-2)^(n-1) = 33`