Question

What is the sum of the series?

Answer 1

Answer:

44

Step-by-step explanation:

substitute k = 1, 2, 3, 4 into 2k² - 4 and sum the terms

k = 1 : 2(1)² - 4 = 2 - 4 = - 2

k = 2 : 2(2)² - 4 = 8 - 4 = 4

k = 3 : 2(3)² - 4 = 18 - 4 = 14

k = 4 : 2(4)² - 4 = 32 - 4 = 28

sum = - 2 + 4 + 14 + 28 = 44

Answer 2

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!