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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Chapter
Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

A sequence is defined recursively by a n + 1 = 3 a n n , a 1 = 2 . Find the first six terms of the sequence.

To determine

The first six terms of the sequence.

Explanation

Given:

The first term of the sequence is 2 and the nth sequence is given as,

an+1=3ann

Approach:

The nth term of a sequence may depend on some or all the terms preceding it. A sequence defined in this way is called recursive.

Calculation:

Calculate the second term of the sequence.

Substitute 1 for n and 2 for a1 in the nth sequence to calculate the second term.

a2=3a11=3(2)1=5

Calculate the third term of the sequence.

Substitute 2 for n and 5 for a2 in the nth sequence to calculate the third term.

a3=3a22=3(5)2=13

Calculate the fourth term of the sequence.

Substitute 3 for n and 13 for a3 in the nth sequence to calculate the fourth term.

a4=3a33=3(13)3=36

Calculate the fifth term of the sequence

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Chapter 13 Solutions

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