Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
$\sum_{i = 1}^{16} (3 i + 2)$

검증된 단계별 안내

Identify the first term $a_1$ and the common difference $d$ of the arithmetic sequence. These are essential to use the sum formula.

Recall the formula for the sum of the first $n$ terms of an arithmetic sequence: \[ S_n = \frac{n}{2} \times (2a_1 + (n - 1)d) \]

Determine the number of terms $n$ you need to sum, based on the problem's given range or limits.

Substitute the values of $a_1$, $d$, and $n$ into the sum formula to set up the expression for $S_n$.

Simplify the expression step-by-step to find the sum of the first $n$ terms, but do not calculate the final numeric value unless asked.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference to the previous term. Understanding this pattern is essential for identifying terms and applying formulas related to sums.

Sum of the First n Terms of an Arithmetic Sequence

This formula calculates the total of the first n terms in an arithmetic sequence. It is given by S_n = n/2 * (2a_1 + (n-1)d), where a_1 is the first term and d is the common difference, enabling efficient summation without adding each term individually.

Summation Notation (Sigma Notation)

Summation notation uses the Greek letter sigma (∑) to represent the sum of a sequence of terms. It provides a concise way to express adding multiple terms, which is crucial for interpreting and solving problems involving series.

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. ∑i=116(3i+2)\(\sum\)_{i=1}^{16} (3i + 2)