A sequence is defined by the recursive function f (n + 1) = 1/2f (n). If f (3) = 9, what is f (1) ?

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Mathematics

Kinley

27 September, 19:17

A sequence is defined by the recursive function f (n + 1) = 1/2f (n). If f (3) = 9, what is f (1) ?

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Moses Russell · Answer 1

To find f (1) it might be a good idea to see what the problem is actually telling us. if f (3) = 9 ... if we put that into the original function that means that

f (3 + 1) = 1/2f (3) so f (4) = 1/2f (3) since f (3) = 9 then f (4) = 4.5 ... so it is one half of f (3) ... now to get to f (1) you need to do the opposite. f (2) will be twice f (3) and so on.

f (4) = 4.5

f (3) = 9

f (2) = 18

f (1) = 36

so f (1) = 36