Question

What is the sum of the series?

Answer 1

Heya!

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Things to know before we solve:

The "6" at the top means that the the sequence only goes to the 6th term.

k = 3 represents that the sequence starts with the 1st term.

(-2k + 5) represents the rule of the sequence, we can substitute 3, 4, 5, and 6 to solve for the terms of the sequence.

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Solving for each term:

3rd term:

-2(3) + 5

-6 + 5

-1

4th term:

-2(4) + 5

-8 + 5

-3

5th term:

-2(5) + 5

-10 + 5

-5

6th term:

-2(6) + 5

-12 + 5

-7

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Simplifying:

Write these terms in expanded form:

(-1) + (-3) + (-5) + (-7)

Find the sum of the series:

(-1) + (-3) + (-5) + (-7) = -16

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Answer:

The sum of the series is -16

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Best of Luck!

Answer 2

For this case we must find the sum of the given series. For this we must expand the series for each value of k.

`(-2 (3) +5) + (- 2 (4) +5) + (- 2 (5) +5) + (- 2 (6) +5) =\\(-6 + 5) + (- 8 + 5) + (- 10 + 5) + (- 12 + 5) =`

Different signs are subtracted and the sign of the major is placed, while equal signs of sum and the same sign is placed.

`-1-3-5-7 =\\-16`

The value of the series is -16

ANswer:

-16