/*! 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 664 Find the sum of the first 20 ter... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 22: Problem 664

Find the sum of the first 20 terms of the arithmetic progression \(-9,-3,3, \ldots\)

Short Answer

Expert verified
The sum of the first 20 terms of the arithmetic progression \(-9, -3, 3, \ldots\) is 960.

Step by step solution

01

Identify the First Term

The first term of the given AP is -9. So, we have \(a_1 = -9\).
02

Determine the Common Difference

In an arithmetic progression, the common difference (d) is the difference between consecutive terms. In our given AP, the second term is -3, and the third term is 3. To find the common difference, we can subtract the first term from the second term or the second term from the third term: \(d = -3 - (-9) = -3 + 9 = 6\) or \(d = 3 - (-3) = 3 + 3 = 6\) So, the common difference of the given AP is 6.
03

Find the nth Term

To find the 20th term of the AP, we use the formula: \(a_n = a_1 + (n-1)d\) where \(a_n\) is the nth term, \(a_1\) is the first term, n is the number of terms, and d is the common difference. Using the values we obtained in Steps 1 and 2, we can now find the 20th term: \(a_{20} = -9 + (20-1)6\) \(= -9 + (19)6\) \(= -9 + 114\) \(= 105\) So, the 20th term of the given AP is 105.
04

Find the Sum of the first 20 Terms

Now that we have the first term, the 20th term, and the number of terms, we can use the sum formula for arithmetic progressions to find the sum of the first 20 terms: \(S_n = \frac{n}{2}(a_1 + a_n)\) Using the values for \(a_1\), \(a_n\), and n: \(S_{20} = \frac{20}{2}(-9 + 105)\) \(= 10(96)\) \(= 960\) So, the sum of the first 20 terms of the given arithmetic progression is 960.

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

Express \(.423\) as a rational fraction.

The sums of n terms of two arithmetic progressions are in the ratio of \(7 \mathrm{n}+1: 4 \mathrm{n}+27 ;\) find the ratio of their 11 th terms.

Find \(\mathrm{a}_{\mathrm{n}}\) for the sequence \(1,4,7,10, \ldots\)

Find the sum of the infinite geometric progression: \(2,1,1 / 2,1 / 4, \ldots\)

If the 8th term of a geometric progression is 16 and the common ratio is \(-3\), what is the 12 th term?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

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.