Question

1,2,5,26 calculate the missing number?

Answer 1

1²+1=2
2²+1=5
5²+1=26
26²+1=677

Answer 2

Try to find connections between the numbers.

2 - 1 = 1

5 - 2 = 3

12 - 5 = 7

29 - 12 = 17

Is the difference seems to be every two prime numbers? 1, 2, 3, 5, 7, 11, 13, 17 - no

1 + 2*2 = 5

2 + 5*2 = 12

5 + 12*2 = 29

The formula is, with x being the place in the sequence and y or f(x) being the output:

f(1) = 1, else f(x) = f(x - 2) + 2f(x-1)

Assume all numbers in the sequence before 1 are 0.

Therefore, we can substitute x with 6, because we are looking for the sixth number in the sequence.

f(6) = f(4) + 2f(5)

Since we know f(4) was 12 and f(5) was 29, we substitute those.

f(6) = 12 + 58

f(6) = 70