Question 246753
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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Substitute 2 for n:

a<sub>n</sub>=-2a<sub>n-1</sub>+2

a<sub>2</sub>=-2a<sub>2-1</sub>+2

a<sub>2</sub>=-2a<sub>1</sub>+2

Now substitute 2 for a<sub>1</sub> since that is given:

a<sub>2</sub>=-2(2)+2

a<sub>2</sub>=-4+2

a<sub>2</sub>=-2 

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Substitute 3 for n:

a<sub>n</sub>=-2a<sub>n-1</sub>+2

a<sub>3</sub>=-2a<sub>3-1</sub>+2

a<sub>3</sub>=-2a<sub>2</sub>+2

Now substitute -2 for a<sub>2</sub> since that is what
we just calculated:

a<sub>3</sub>=-2(-2)+2

a<sub>3</sub>=4+2

a<sub>3</sub>=6 

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Substitute 4 for n:

a<sub>n</sub>=-2a<sub>n-1</sub>+2

a<sub>4</sub>=-2a<sub>4-1</sub>+2

a<sub>4</sub>=-2a<sub>3</sub>+2

Now substitute 6 for a<sub>3</sub> since that is what
we just calculated:

a<sub>4</sub>=-2(6)+2

a<sub>4</sub>=-12+2

a<sub>4</sub>=-10 

So the first four terms, a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>, a<sub>4</sub> are 2, -2, 6, and -10, respectively. 

Edwin</pre>