/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 43 Find the sum of the even integer... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 43

Find the sum of the even integers between 21 and 45

Short Answer

Expert verified
The sum of the even integers between 21 and 45 is 396

Step by step solution

01

Find the first and last even numbers within the range

The first step is to find the smallest even number greater than 21 and the largest even number less than 45. The first even number in this range would be 22 and the last would be 44
02

Calculate number of terms

Next, find the number of even numbers within this range. Since this sequence of even integers has a common difference of 2, the number of terms, \(n\), can be calculated as \((l - a)/2 + 1 \), where \(a\) is the first term and \(l\) is the last term. So, \(n = (44-22)/2 + 1 = 12\)
03

Apply the sum formula

Now, apply the formula for the arithmetic series sum, \(S_n = n/2 * (a+l)\), where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term. Substituting values into the formula gives \(S_n = 12/2 * (22 + 44) = 6 * 66 = 396\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explaining the Concepts Explain how to find and probabilities with independent events. Give an example.

Explain how to find the general term of a geometric sequence.

In the sequence \(21,700,23,172,24,644,26,116, \ldots,\) which term is \(314,628 ?\)

Explaining the Concepts What are mutually exclusive events? Give an example of two events that are mutually exclusive.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.