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Chapter 12: Q 44. (page 809)

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

a1=-2;an=n+3an-1

Short Answer

Expert verified

The first five terms of the recursively defined sequence are-2,-4,-9,-23,and-64.

Step by step solution

01

Step 1. Write the given information.

The given recursively defined sequence is:

a1=-2an=n+3an-1

02

Step 2. Determine the first term and find out the second term.

The first term is a1=3.

Now substitute 2 for nin the given formula an=n+3an-1to get the second term,

role="math" localid="1646730495162" a2=2+3a2-1=2+3a1=2+3-2=2-6=-4

03

Step 3. Find the 3rd and 4th terms.

Similarly substitute 3, 4 for nin the given formula to get the third and fourth term,

a3=3+3a3-1=3+3a2=3+3-4=-9a4=4+3a4-1=4+3a3=4+3-9=4-27=-23

04

Step 4. Find the 5th term.

Now substitute 5 for nin the given formula to get the 5th term,

a5=5+3a5-1=5+3a4=5+3-23=5-69=-64

Therefore, the first five terms are-2,-4,-9,-23,-64.

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