Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q16.

Expert-verified

Algebra 1

Found in: Page 523

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Find the next three terms of each arithmetic sequence.
$16, 4, - 8, - 20, ...$

The next three terms of the given arithmetic sequence are $- 32, - 44$ and $- 56$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Find the first term and the common difference of the given arithmetic sequence.

The given arithmetic sequence is: $16, 4, - 8, - 20$ .

From the given arithmetic sequence, it can be noticed that the first, second, third, and fourth terms of the arithmetic sequence are $16, 4, - 8$ and $- 20$ respectively.

The common difference of the arithmetic sequence is the difference between the succeeding term and its preceding term.

Therefore, the common difference $(d)$ of the given arithmetic sequence is:

$d = 4 - 16 = - 12$

Therefore, the first term and the common difference of the given arithmetic sequence are 16 and $- 12$ respectively.

Step 2. Find the next three terms of the given arithmetic sequence.

The $n th$ term $(a_{n})$ of the given arithmetic sequence is given by:

$a_{n} = a_{1} + (n - 1) d$ , where $a_{1}$ is the first term and $d$ is a common difference.

The next three terms of the given arithmetic sequence are fifth, sixth, and seventh terms.

Therefore, the next three terms of the given arithmetic sequence having $a_{1} = 16$ and $d = - 12$ are:

$a_{5} = a_{1} + (5 - 1) d$

$= 16 + (4) (- 12) = 16 - 48 = - 32$

$a_{6} = a_{1} + (6 - 1) d$

$= 16 + (5) (- 12) = 16 - 60 = - 44$

$a_{7} = a_{1} + (7 - 1) d$

$= 16 + (6) (- 12) = 16 - 72 = - 56$

Therefore, the next three terms of the given arithmetic sequence are $- 32, - 44$ and $- 56$ .

Most popular questions for Math Textbooks

Graph each function. Find the y-intercept, and state the domain and range.

$y = 2^{x}$

Which of the following is an equation for the line that passes through $(2, - 5)$ and is perpendicular to $2 x + 4 y = 8$ ?

$A y = 2 x + 10 B y = - \frac{1}{2} x - 4 C y = 2 x - 9 D y = - 2 x - 1$

Christopher is repairing the roof on a shed. He accidentally dropped a box of nails from a height of 14 feet. This is represented by the equation $h = - 16 t^{2} + 14,$ where $h$ the height in feet and $t$ is the time in seconds. Describe how the graph is related to .

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

Use the graph of the quadratic equation shown below to answer each question.

A What is the vertex?

B What is the $y$ -intercept?

C What is the axis of symmetry?

D What are the roots of the corresponding quadratic equation?

Write an expression for the area of the rectangle below.

$F 10 b^{5} c^{5} - 3 b c G 10 b^{5} c^{5} - 15 b^{2} c^{3} H 2 b^{5} c^{5} - 3 b^{2} c^{3} J 10 b^{4} c^{6} - 15 b c^{2}$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free