Which number is the next logical number in the following sequence of numbers: 2, 6, 14, 30,...

Solution:

A geometric sequence has consecutive terms with a common ratio between them. After a careful examination of the sequence given it can be seen that the differences between the consecutive terms are in a geometric progression as shown below:

Difference of consecutive terms: (6-2), (14 - 6), (30 - 14) ....

4, 8,16,

The next difference should be 32. Therefore the next logical number in the sequence will be :

30 + 32 = 62

Which number is the next logical number in the following sequence of numbers: 2, 6, 14, 30,...

Summary:

The next logical number of the sequence will be 62.