Multiple choice

In an arithmetic series, $a_1 = 7$ and $a_{12}=29$. Find the sum of the first 12 terms.

  1. $116$
  2. $216$
  3. $316$
  4. $416$
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B Correct answer
Explanation

The sum of an arithmetic series is given by S = (n/2)(a_1 + a_n). Substituting the given values, S = (12/2)(7 + 29) = 6 * 36 = 216.

AI explanation

First, determine the common difference using the nth term formula: $29 = 7 + 11d$, which means $11d = 22$ and $d = 2$. Next, use the arithmetic series sum formula $S_n = n/2 \times (a_1 + a_n)$ to find the sum of the first 12 terms: $S_{12} = 12/2 \times (7 + 29)$. This simplifies to $6 \times 36$, which equals 216. The result is 216.

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