How to make pattern ?
4, 77, 498, 2515, 10076, 30237, .........

77-4=73
498-77=421
2515-4982017
how to solve these type of question in few second ?

Just ask someone like DGElder who will be more than willing to solve it for you and just give you the answer.

 

You have a slight typo or math error, @WBahn , I get...
5205, 3008, x-------, 948, 605, 480, 453, 452, 452

Oh, forgot to mention, if we keep going the sequence doesn't repeat 452. It would be

5205, 3008, x, 948, 605, 480, 453, 452, 453, 480, 605, 948, x, 3008, 5205, 8580, 13493, ...

 

How to make pattern ?
4, 77, 498, 2515, 10076, 30237, .........

77-4=73
498-77=421
2515-4982017
how to solve these type of question in few second ?

Note that the differences are all prime numbers.

 

Note that the differences are all prime numbers.

Except for the step for the unknown number, when the step change is 9 cubed.

The differences in the sequence are the cubes of a sequence of odd numbers.

605-480=125 is 5^3
948-605=343 is 7^3
x-948 = 729 is 9^3
3008 - x is 11^3
5205-3008=2197 is 13^3

x= 1677

 

Except for the step for the unknown number, when the step change is 9 cubed.

Note that RRitesh, as usual, moved onto a completely different problem.

None of the differences in the original problem were prime (since they were all cubes of some number and since 1 is not prime).