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Chapter 12: Q 42. (page 809)

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

a1=2;an=-an-1

Short Answer

Expert verified

The first five terms of the recursively defined sequence are2,-2,2,-2,and2.

Step by step solution

01

Step 1. Write the given information.

The given recursively defined sequence is:

a1=2an=-an-1

02

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

The first term is a1=2.

Now substitute 2 for nin the given formulaan=-an-1 to get the second term,

a2=-a2-1=-a1=-2

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=-a3-1=-a2=-(-2)=2a4=-a4-1=-a3=-2=-2

04

Step 4. Find the 5th term.

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

a5=-a5-1=-a4=--2=2

Therefore, the first five terms arerole="math" localid="1646729168242" 2,-2,2,-2,2.

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