Question 116640
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Give the recursive formula for the series 4,16,64...
0 solutions

16, the 2nd term, is 4 times the first term 4
64, the 3rd term, is 4 times the second term 16

So apparently,

Each term = 4 times the previous term

There are two acceptable ways to write that sentence
as a recursion formula:

If you think of it as

The nth term is 4 times the (n-1)st term

then the recursion formula is
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a<sub>n</sub> = 4·a<sub>n-1</sub>, a<sub>1</sub> = 4 where n > 1
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Or if you think of it as

The (n+1)st term is 4 times the nth term

then the recursion formula is
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a<sub>n+1</sub> = 4·a<sub>n</sub>, a<sub>1</sub> = 4 where n > 0
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They are both correct, and equivalent.

Edwin</pre>