In Exercises 29–42, find each indicated sum. 9Σi=5 11

Verified step by step guidance

1. Identify the summation notation: $\sum _{i=5}^{9}11$.
2. Understand that the expression $11$ is a constant term, meaning it does not depend on $i$.
3. Determine the number of terms in the summation: from $i=5$ to $i=9$, there are 5 terms (5, 6, 7, 8, 9).
4. Since the term is constant, the sum is simply the constant multiplied by the number of terms: $11\times 5$.
5. Calculate the product to find the sum.

Key Concepts

Summation Notation

Summation notation, represented by the Greek letter sigma (Σ), is a concise way to express the sum of a sequence of numbers. The notation Σi=a^b f(i) indicates that you sum the function f(i) from i = a to i = b. Understanding this notation is crucial for interpreting and calculating sums in algebra.

Constant Functions

A constant function is a function that always returns the same value regardless of the input. In the given problem, the function is f(i) = 11, which means that for every value of i, the output is 11. Recognizing that the sum of a constant over a range can be simplified is essential for efficient calculation.

Arithmetic Series

An arithmetic series is the sum of the terms of an arithmetic sequence, where each term differs from the previous one by a constant. In this case, since the function is constant, the sum can be calculated by multiplying the constant value by the number of terms being summed. This concept helps in quickly finding the total without needing to add each term individually.