What is the sum of the series?

For this case we must find the sum of the given series. For this we must expand the series for each value of k.
[tex](-2 (3) +5) + (- 2 (4) +5) + (- 2 (5) +5) + (- 2 (6) +5) =\\(-6 + 5) + (- 8 + 5) + (- 10 + 5) + (- 12 + 5) =[/tex]
Different signs are subtracted and the sign of the major is placed, while equal signs of sum and the same sign is placed.
[tex]-1-3-5-7 =\\-16[/tex]
The value of the series is -16
ANswer:
-16
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!