SOLUTION: write the first four terms of the sequence defined by the recursion formula a<sub>1</sub>=2 a<sub>n</sub>=-2a<sub>n-1</sub>+2, n > 1

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Question 246753: write the first four terms of the sequence defined by the recursion formula
a1=2
an=-2an-1+2, n > 1
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
write the first four terms of the sequence defined by the recursion formula
a1=2
an=-2an-1+2, n > 1

Substitute 2 for n:

an=-2an-1+2

a2=-2a2-1+2

a2=-2a1+2

Now substitute 2 for a1 since that is given:

a2=-2(2)+2

a2=-4+2

a2=-2 

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Substitute 3 for n:

an=-2an-1+2

a3=-2a3-1+2

a3=-2a2+2

Now substitute -2 for a2 since that is what
we just calculated:

a3=-2(-2)+2

a3=4+2

a3=6 

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Substitute 4 for n:

an=-2an-1+2

a4=-2a4-1+2

a4=-2a3+2

Now substitute 6 for a3 since that is what
we just calculated:

a4=-2(6)+2

a4=-12+2

a4=-10 

So the first four terms, a1, a2, a3, a4 are 2, -2, 6, and -10, respectively. 

Edwin