/*! 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 19 Find the indicated term of each ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 19

Find the indicated term of each sequence. $$ a_{n}=3 n^{2}(9 n-100) ; a_{11} $$

Short Answer

Expert verified
The term \(a_{11}\) is -363.

Step by step solution

01

- Understanding the given sequence formula

The problem provides a formula for the nth term of a sequence: \[a_{n}=3n^{2}(9n-100)\].Here, you need to determine the term when \(n = 11\).
02

- Substitute the given value of n into the formula

Insert \( n = 11 \) into the formula:\[ a_{11} = 3(11)^{2}(9(11)-100).\]
03

- Simplify inside the parentheses

Calculate the expression inside the parentheses:\[9(11) - 100 = 99 - 100 = -1.\]
04

- Calculate the power of 11

Compute \(11^{2}\):\[11^{2} = 121.\]
05

- Multiply all components

Now multiply all the terms together:\[3 \times 121 \times (-1) = 3 \times 121 \times -1 = -363.\]
06

- Write the final result

Thus, the indicated term \(a_{11}\) is \[a_{11} = -363.\]

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.

sequence formula
A sequence formula is an equation that defines the nth term of a sequence. In our case, the formula is given as a_{n} = 3n^{2}(9n - 100).This formula helps to find the position of any term in the sequence based on its index number, n. The structure includes constants and variables which determine the behavior of the sequence. Formulas like this are essential in arithmetic and geometric sequences.
nth term
The nth term represents the position of an element in a sequence. For this problem, we need to find the 11th term, denoted as a_{11}. Inserting 'n' into the formula is key to pinpoint the value required. This means substituting n with 11 in our given formula. The nth term tells us where exactly we are in the sequence and allows us to calculate its specific value.
substitution
Substitution involves replacing a variable in an equation with a given number. Here, we substitute n with 11: a_{11} = 3(11)^{2}(9(11) - 100).This step is crucial because it personalizes the general formula to find a specific value, transforming the abstract into something concrete. The operation helps simplify understanding and calculating the term in focus.
arithmetic operations
Arithmetic operations help in solving any parts of the sequence formula. We need to deal with addition, subtraction, multiplication, and exponentiation. For example:1. Calculate the power: 11^{2} making 1212. Inside the parentheses: 9(11) - 100 would be 99 - 100 equals -13. Finally, multiply: 3 * 121 * (-1) results in -363.These operations are straightforward but require attention to detail to ensure accurate computation.

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 term containing \(\frac{1}{x^{1 / 6}}\) of $$\left(\sqrt[3]{x}-\frac{1}{\sqrt{x}}\right)^{7}$$

Rewrite each sum using sigma notation. Answers may vary. $$ 4-9+16-25+\cdots+(-1)^{n} n^{2} $$

Prove that $$\left(\begin{array}{l}{n} \\\\{r}\end{array}\right)=\left(\begin{array}{c}{n} \\\\{n-r} \end{array}\right)$$for any whole numbers \(n\) and \(r .\) Assume \(r \leq n\)

Find the indicated term for each geometric sequence. \(\sqrt{3}, 3,3 \sqrt{3}, \ldots ;\) the 10 th term

Find an equation of the line satisfying the given conditions. Slope \(\frac{1}{3}, y\) -intercept \((0,10)\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision 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.