Let f be a function dened on the set of integers such that f(1) = 5

and f(x + 1) = 2f(x) + 1 for all integers x. What is the value of

f(7) - f(0)?

i bet the answer is 381 but i couldn't make how to the solution is done.

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- November 24th 2010, 05:54 PMrcsfunction equation functions
Let f be a function dened on the set of integers such that f(1) = 5

and f(x + 1) = 2f(x) + 1 for all integers x. What is the value of

f(7) - f(0)?

i bet the answer is 381 but i couldn't make how to the solution is done. - November 24th 2010, 05:59 PMmr fantastic
- November 24th 2010, 06:20 PMpickslides
- November 25th 2010, 05:10 AMrcs
a friend of mine told me that it is 381,,, but she couldnt show to me how she solved it,,, that is why i just guessed it. hope i could get the right flow of the solution. thanks

- November 25th 2010, 05:17 AMPlato
- November 25th 2010, 05:57 AMSoroban
Hello, rcs!

If you can read the problem, you can baby-talk your way through it.

Quote:

The first term is 5.

Each subsequent term is twice the preceding term, plus 1.

We have:

. .

What is ?

Since , we have: .

Therefore: .

- November 25th 2010, 10:47 PMrcs
thanks you so so much Soroban!!! ilove you all here! :) i can now have a good night sleep