QUESTION: 2 7 25 91. whats the next number?
I don't know if this will be the answer, but I have found a rule that appplies to the above 4 numbers.
The 4 numbers are: 2 7 25 91.
These numbers can be manipulated as follows.
4*2 - 1 = 8 - 1 = 7
4*7 - 3 = 28 - 3 = 25
4*25 - 9 = 100 - 9 = 91
Letting a_1 = 2, a_2 = 7, a_3 = 25 and a_4 = 91, we can rewrite the original 4 expressions as,
4*a_1 - 3^0 = a_2
4*a_2 - 3^1 = a_3
4*a_3 - 3^2 = a_4
From which we get the rule,
a_n = 4*a_(n-1) - 3^(n-2), n>= 2, a_1 = 2
So, the next number is a_5 = 4*a_4 - 3^3
a_5 = 4*91 - 27 = 364 - 27 = 337
Next number is: 337
p.s. the folowing rule also works, and give a_5 = 337!
a_n = 3*a_(n-1) + 4^(n-2), n>= 2, a_1 = 2