In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 10 Σ (i = 1) 5 · 2^i

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the sequence is defined by the formula 5 · 2^i, where 5 is the initial term and 2 is the common ratio. Understanding this concept is crucial for identifying the terms of the sequence and calculating their sum.

The sum of the first n terms of a geometric series can be calculated using the formula S_n = a(1 - r^n) / (1 - r), where S_n is the sum, a is the first term, r is the common ratio, and n is the number of terms. This formula allows for efficient calculation of the sum without needing to add each term individually, which is essential for solving the given problem.

Sigma notation is a concise way to represent the sum of a sequence of terms. It uses the Greek letter sigma (Σ) to indicate summation, along with limits that specify the starting and ending indices. In the given question, Σ (i = 1 to 10) indicates that we are summing the terms from i = 1 to i = 10, which is fundamental for understanding how to apply the sum formula correctly.