   Chapter 13.CR, Problem 36E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Arithmetic and Geometric Sequences Find the values of x and y for which the sequence 2 , x , y , 17 , … is, (a) arithmetic (b) geometric

To determine

(a)

The values of x and y when the sequence is arithmetic.

Explanation

Given:

The given sequence is,

2, x, y, 17, …

Approach:

An arithmetic sequence is a sequence of the form,

a, a+d, a+2d, a+3d, …

Here, a is the first term and d is the common difference which is the difference between two consecutive terms.

The nth term of an arithmetic sequence is,

an=a+(n1)d(1)

Calculations:

Consider the sequence 2, x, y, 17, …

17 is the fourth term of the sequence so substitute 4 for n and 17 for a4 in equation (1).

To determine

(b)

The values of x and y when the sequence is geometric.

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