Question

1,5,15,29,? what is the next number

Answer 1

The above given series can have multiple answers for the next term of the series. For instance, one such answer can be calculated using the principle of Continuous Difference Theorem.
 
Looking at each successive two terms, their differences are calculated as follows:
 
5 – 1 = 4
15 – 5 = 10
29 – 15 = 14
 
Again, the difference between the successive differences which were previously calculated is:
 
10 – 4 = 6
14 – 10 = 4
 
We notice that this follows the decreasing multiples of two. The next multiple of two is 2. Hence, the next difference will be 16. Adding 16 to the last term of the series given in the question, we get the next term to be 45.
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Answer 2

Given Series is 1,5,15,29

= > 1 + 4 = 5

= > 5 + 10 = 15

= > 15 + 14 = 29

= > 29 + 16 = 45.

The difference between the 1st and 2nd sum is 6(10 - 4)

The difference between the 2and and 3rd sum is 4(14 - 10).

As u can see, the difference between them keeps on decreasing.

The next difference should be 2. So, the number should be 16.(16 - 14).



Therefore the next number is 45.



Hope it helps!