/*! 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 25 Find the fifth term of an arithm... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 25

Find the fifth term of an arithmetic sequence whose second term is 8 and whose third term is 14 .

Short Answer

Expert verified
The fifth term of the arithmetic sequence is 26.

Step by step solution

01

Find the common difference

Since it's an arithmetic sequence, we know that the difference between consecutive terms is constant. We can use the second and third terms to find the common difference: \(d = 14 - 8 = 6\)
02

Find the first term

To find the fifth term, we first need to find the first term of the sequence. Using the common difference, we can work backwards from the second term (8) to find the first term (a鈧�): \(a鈧� = 8 - 6 = 2\)
03

Use the formula to find the fifth term

Now that we have the first term (a鈧�) and the common difference (d), we can use the formula for the nth term of an arithmetic sequence: \(a_n = a鈧� + (n-1)d\) We want to find the fifth term, so n = 5: \(a_5 = 2 + (5-1)(6)\)
04

Calculate the fifth term

Now we just need to plug in the values and calculate the answer: \(a_5 = 2 + (4)(6)\) \(a_5 = 2 + 24\) \(a_5 = 26\) So, the fifth term of the arithmetic sequence is 26.

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

Find the coefficient of \(w^{198}\) in the expansion of \((w+3)^{200}\).

Restate the symbolic version of the formula for evaluating an arithmetic series using summation notation.

Write the series using summation notation (starting with \(k=1\) ). Each series is either an arithmetic series or a geometric series. $$ \frac{7}{16}+\frac{7}{32}+\frac{7}{64}+\cdots+\frac{7}{2^{25}} $$

Write the series explicitly and evaluate the sum. $$ \sum_{k=0}^{3} \log \left(k^{2}+2\right) $$

Evaluate the geometric series. $$ \sum_{k=1}^{40} \frac{3}{2^{k}} $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.