/*! 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 13 Find the indicated term for each... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 13

Find the indicated term for each sequence. $$ a_{n}=-9 n+2 ; \quad a_{8} $$

Short Answer

Expert verified
The indicated term is \( a_{8} = -70 \).

Step by step solution

01

Identify the general formula

The general formula for the sequence is given as \[ a_n = -9n + 2 \]
02

Determine the specific term

Identify the term required in the sequence. Here, it is \( a_8 \). This means substituting \( n = 8 \) into the general formula.
03

Substitute and calculate

Substitute \( n = 8 \) in the formula \[ a_{8} = -9(8) + 2 \] Perform the calculations: \[ a_{8} = -72 + 2 \] \[ a_{8} = -70 \]

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

arithmetic sequences
In mathematics, sequences are collections of numbers arranged in a specific order. One common type is called an arithmetic sequence. This kind of sequence has a specific pattern: the difference between consecutive terms is always the same. This consistent difference is known as the 'common difference'. For instance, in the sequence 2, 5, 8, 11, the common difference is 3. Each term increases by 3 from the previous one.
general formula
To describe an arithmetic sequence, we use a general formula. This formula helps us find any term in the sequence quickly. For an arithmetic sequence, the general formula is: \( a_n = a_1 + (n - 1)d \). Here, \( a_n \) represents the term we want to find, \( a_1 \) is the first term in the sequence, \( n \) is the position of the term, and \( d \) is the common difference. This formula gives a straightforward method to find any term if you know the first term and the common difference.
term calculation
Calculating a term within an arithmetic sequence involves using the general formula. For instance, if we want to find the 8th term in a sequence, we set \( n = 8 \). Using the formula from our example: \( a_n = -9n + 2 \), we substitute 8 for \( n \). This substitution yields the expression: \( a_8 = -9(8) + 2 \). We then perform the necessary calculations to find \( a_8 = -72 + 2 = -70 \).
substitution in algebra
Substitution in algebra involves replacing variables with their specific values to simplify or solve expressions. In our sequence example, we substituted \( n = 8 \) into the general formula \( a_n = -9n + 2 \). This process involves:
  • Identifying the variable to replace.
  • Substituting the identified value into the formula.
  • Simplifying the expression to find the result.
Substitution is a crucial technique widely used not just in sequences, but in solving a variety of algebraic problems.

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

Write out the first five terms of each sequence. $$ a_{n}=\frac{-2}{n^{2}} $$

Use the formula for \(a_{n}\) to find the general term of each arithmetic sequence. $$ a_{1}=5, d=3 $$

Write the first five terms of each arithmetic sequence. $$ a_{1}=-3, d=-5 $$

Find a general term \(a_{n}\) for the given terms of each sequence. $$ 7,14,21,28, \dots $$

Solve each problem. A stack of firewood has 28 pieces on the bottom, 24 on top of those, then \(20,\) and so on. If there are 108 pieces of wood, how many rows are there? (Hint: \(n \leq 7\).)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.