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Question Find the sum of the first 34 terms of the following series, to the nearest integer. \[ 8,12,16, \ldots \] Answer Attempt t out of 3 Submit Answer

Ask by Love Graham. in the United States
Mar 14,2025

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The sum of the first 34 terms is 2516.

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The series given is an arithmetic series where the first term \(a = 8\) and the common difference \(d = 12 - 8 = 4\). The formula for the sum \(S_n\) of the first \(n\) terms of an arithmetic series is: \[ S_n = \frac{n}{2} \times (2a + (n-1)d) \] For \(n = 34\): \[ S_{34} = \frac{34}{2} \times (2 \times 8 + (34-1) \times 4) \] Calculating inside the parentheses: \[ 2 \times 8 = 16 \] \[ (34-1) \times 4 = 33 \times 4 = 132 \] Thus, \[ S_{34} = 17 \times (16 + 132) \] Calculating further: \[ 16 + 132 = 148 \] So, \[ S_{34} = 17 \times 148 = 2516 \] Therefore, the sum of the first 34 terms is 2516, which is already an integer. The final answer is: 2516

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