/*! 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 75 Explain how to find the sum of t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 75

Explain how to find the sum of the first \(n\) terms of an arithmetic sequence without having to add up all the terms.

Short Answer

Expert verified
The sum of the first \(n\) terms of an arithmetic sequence can be found using the formula \(S_n = n/2 * (a + l)\), where \(S_n\) is the sum, \(n\) is number of terms, \(a\) is the first term and \(l\) is the last term. The first term \(a\) and last term \(l = a +(n-1)d\) can be easily identified in the sequence and substituted in the formula to find the sum.

Step by step solution

01

Understand the Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant. This simply means that the numbers progress in a linear or straight-line manner. For example, the sequence '1, 3, 5, 7' is an arithmetic sequence with a common difference of 2.
02

Identify the Elements in the Formula

Before using the formula, it's necessary to identify the values in the given sequence. The first term \(a\) is just the first number in the sequence and the last term \(l\) will be the nth term in the sequence, which is \(a + (n-1)d\) where \(d\) is the common difference.
03

Use the Sum Formula

Once all the elements are identified, substitute the values of \(n\), \(a\) and \(l\) in the sum formula \(S_n = n/2 * (a + l)\). This will give the sum of the first \(n\) terms of an arithmetic sequence without having to add up all the terms individually.

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

Use the formula for \(_{n} C_{r}\) to solve Of the 100 people in the U.S. Senate, 18 serve on the Foreign Relations Committee. How many ways are there to select Senate members for this committee (assuming party affiliation is not a factor in selection)?

Make Sense? In Exercises \(78-81,\) determine whether each statement makes sense or does not make sense, and explain your reasoning. The sequence for the number of seats per row in our movie theater as the rows move toward the back is arithmetic with \(d-1\) so people don't block the view of those in the row behind them.

A mathematics exam consists of 10 multiple-choice questions and 5 open-ended problems in which all work must be shown. If an examinee must answer 8 of the multiple-choice questions and 3 of the open-ended problems, in how many ways can the questions and problems be chosen?

Write an original problem that can be solved using the Fundamental Counting Principle. Then solve the problem.

Solve by the method of your choice. A book club offers a choice of 8 books from a list of \(40 .\) In how many ways can a member make a selection?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

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.