What is the sum of the first 21 terms of the series 1 + 4 + 7 + 10 + 13 + 16 …?Select one:a. 642b. 645c. 648d. 651
Question
What is the sum of the first 21 terms of the series 1 + 4 + 7 + 10 + 13 + 16 …?
Select one:
- a. 642
- b. 645
- c. 648
- d. 651
Solution
The given series is an arithmetic series where the common difference (d) is 3 (4-1, 7-4, 10-7, etc.).
The sum (S) of the first n terms of an arithmetic series can be calculated using the formula:
S = n/2 * (2a + (n-1)d)
where:
- n is the number of terms,
- a is the first term, and
- d is the common difference.
Substituting the given values into the formula:
S = 21/2 * (2*1 + (21-1)*3) S = 10.5 * (2 + 60) S = 10.5 * 62 S = 651
So, the sum of the first 21 terms of the series is 651 (option d).
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