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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

15-20 ■ Recursive Sequence A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.

a n = 2 ( a n 1 + 3 ) and a 1 = 4

To determine

The first five terms of the sequence an=2(an1+3).

Explanation

Given:

The nth term of the sequence is given as

an=2(an1+3)… (1)

And

a1=4

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:

Substitute 2 for n and 4 for a1 in equation (1), to calculate the second term,

a2=2(a1+3)=2(4+3)=14

Substitute 3 for n and 14 for a2 in equation (1), to calculate the third term,

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