What should come in place of the question mark (?) in the given series? 22,…

Concept: When the differences between consecutive terms of a series themselves increase by a fixed amount (i.e., the second difference is constant), the differences form their own arithmetic progression. The next difference can be found by continuing that arithmetic progression, and the next term is obtained by adding this new difference to the last given term.

Application:

1. 22, 34, 58, 94, 142, ? -> find the consecutive differences: 34-22=12, 58-34=24, 94-58=36, 142-94=48.

2. Compare these differences: 12, 24, 36, 48. Each difference is 12 more than the one before it, so the differences form an arithmetic progression with common difference 12.

3. Continuing this progression, the next difference is 48+12=60.

4. Add this difference to the last given term: 142+60=202.

Cross-check: The differences can also be written as 12x1, 12x2, 12x3, 12x4 for the 1st, 2nd, 3rd and 4th gaps respectively. The 5th gap (between the 5th and 6th terms) then follows the same rule: 12x5=60. Adding this to 142 again gives 142+60=202, confirming the result.