For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

Verified step by step guidance

1. Identify the sequence: The given expression is \( \sum_{i=1}^{17} (5i + 3) \), which represents an arithmetic sequence.
2. Find the first term: Substitute \( i = 1 \) into the expression \( 5i + 3 \) to get the first term.
3. Find the second term: Substitute \( i = 2 \) into the expression \( 5i + 3 \) to get the second term.
4. Find the third term: Substitute \( i = 3 \) into the expression \( 5i + 3 \) to get the third term.
5. Find the last term: Substitute \( i = 17 \) into the expression \( 5i + 3 \) to get the last term.

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. In the given problem, the expression (5i + 3) represents the nth term of the sequence, where 'i' is the term number. Understanding how to identify the first few terms is crucial for solving the problem.

Summation Notation

Summation notation, represented by the sigma symbol (Σ), is a concise way to express the sum of a sequence of terms. In this case, it indicates that we are summing the terms of the sequence from i=1 to i=17. Recognizing how to interpret and manipulate summation notation is essential for calculating the total sum of the specified terms.

Sum of an Arithmetic Series Formula

The formula for the sum of the first n terms of an arithmetic series is S_n = n/2 * (a_1 + a_n), where S_n is the sum, n is the number of terms, a_1 is the first term, and a_n is the last term. This formula allows for efficient calculation of the total sum without needing to add each term individually. Applying this formula correctly is key to finding the indicated sum in the problem.