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Chapter 12: Q 38. (page 809)

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

a1=3;an=4-an-1

Short Answer

Expert verified

The first five terms of the recursively defined sequence are3,1,3,1,and3.

Step by step solution

01

Step 1. Write the given information.

The given recursively defined sequence is:

a1=3an=4-an-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=4-an-1to get the second term,

a2=4-a2-1=4-a1=4-3=1

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=4-a3-1=4-a2=4-1=3a4=4-a4-1=4-a3=4-3=1

04

Step 4. Find the 5th term.

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

a5=4-a5-1=4-a4=4-1=3

Therefore, the first five terms are3,1,3,1,3.

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