Heya!
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Things to know before we solve:
The "4" at the top means that the the sequence only goes to the 4th term.
k = 1 represents that the sequence starts with the 1st term.
(2k² - 4) represents the rule of the sequence, we can substitute 1, 2, 3, and 4 to solve for the terms of the sequence.
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Solving for each term:
1st term:
2(1)² - 4
2(1) - 4
2 - 4
-2
2nd term:
2(2)² - 4
2(4) - 4
8 - 4
4
3rd term:
2(3)² - 4
2(9) - 4
18 - 4
14
4th term:
2(4)² - 4
2(16) - 4
32 - 4
28
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Simplifying:
Write these terms in expanded form:
(-2) + 4 + 14 + 28
Find the sum of the series:
(-2) + 4 + 14 + 28 = 44
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Answer:
The sum of the series is 44
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Best of Luck!
