What is the next number in the sequence? and why ?

5

Since we are given the first 5 terms, we know that the nth term is a quartic polynomial .

So let the nth term be f(n) = a(n-1)(n-2)(n-3)(n-4) + b(n-1)(n-2)(n-3) + c(n-1)(n-2) +d(n-1) + e

f(1) = 5 so e = 5

f(2) = 7 so d + 5 = 7 and so d = 2

f(3) = 7 so 2c +4 +5 = 7 and so c = - 1

f(4) = 2 so 3*2*1*b +3*2*(-1) + 2*3 + 5 = 2 and so b = - 1/2

f(5) = 1 so 4*3*2*1*a +(-1/2)*4*3*2 +(-1)*4*3 + 2*4 +5 = 1 and so a = 1/2

Hence f(6) = (1/2)*5*4*3*2*1 +(-1/2)*5*4*3 +(-1)*5*4 + 2*5 +5 = 25

So the next number in the sequence is 25.

6

6, because it is 6

3, 234,456, 287,801,234,00.023

Because I felt like saying it was.