Question

what is the next number in the series? - 2, 3, 28, 15, 126, 35, __

Answer 1

Given:

2, 3, 28, 15, 126, 35

To find:

The next number in the series.

Solution:

We have to find the pattern of the series to find the next missing number.

The series actually has two patterns.

One for the odd terms i.e. 1st, 3rd, 5th  ....terms..

Other pattern for even terms i.e. 2nd, 4th, 6th ..... terms

Let us consider them separately.

2, 28, 126 , .....

2 is 1 + 1 or $1^3+1$

28 is 27 + 1 or $3^3+1$

126 is 125 + 1 or $5^3+1$

So, next term will be:

$7^3$ + 1 = 343 + 1 = 344

Now, the second pattern:

3, 15, 35, ....

3 = 1 $\times$ 3

15 = 3 $\times$ 5

35 = 5 $\times$ 7

So, next term in this pattern will be:

7 $\times$ 9 = 63

So, the answer is 344.

And the series will be as follows:

2, 3, 28, 15, 126, 35, 344