Can you write a recursive formula without the recurrence relation form?

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Say for the recursive formula 2, 5, 9, 19 , 37...Instead of writing it as an = an-1 + * 2 an-2

can you write it as:

an = 2an + (-1)nJust double checking. I encountered this earlier helping someone and I haven't done recursive formulas in a while..
 
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I think you meant an = 2an-1 + (-1)n

Sure. Your formula is the same as

an = an-1 + (-1)n + an-1
= an-1 + (-1)n + 2an-2 + (-1)n-1
= an-1 + 2an-2