What comes next in the sequence: 5, 13, 29, 61,...?

Solution:

The difference between the successive numbers in the sequence is enumerated below: 5, 13, 29, 61,

13 - 5 = 8 --- (1)

29 - 13 = 16 --- (2),

61 - 29 = 32 --- (3)

If we write down the differences in the manner below:

8, 16, 32,

It is evident from the sequence of the differences above that it is a geometric sequence with a common ratio of 2.

16/8 = 2; 32/16 = 2

Let the next number in the sequence be x. Therefore the next number of the sequence of differences will be:

x/32 = 2

x = 64

Therefore the sequence of differences will be 8, 16, 32 and 64

Going back to the original sequence of numbers i.e. 5, 13, 29, 61, the next number in the sequence will be:

61 + 64 = 125

What comes next in the sequence: 5, 13, 29, 61,...?

Summary:

The next number in the sequence: 5, 13, 29, 61, will be 125.