Consider the following series: 10, 17, 24, ... . What is the sum of the first 16 terms of the series?Group of answer choices100078221301236
Question
Consider the following series: 10, 17, 24, ... .
What is the sum of the first 16 terms of the series?
Group of answer choices
- 1000
- 782
- 130
- 1236
Solution
This is an arithmetic series where the common difference (d) is 7 (17-10) and the first term (a) is 10.
The sum (S) of the first n terms of an arithmetic series can be found using the formula:
S = n/2 * (2a + (n-1)d)
Substituting the given values into the formula gives:
S = 16/2 * (2*10 + (16-1)*7) S = 8 * (20 + 105) S = 8 * 125 S = 1000
So, the sum of the first 16 terms of the series is 1000.
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