What should come in place of the question mark (?) in the given series? 5000,…

In a geometric progression, every term is obtained by multiplying the previous term by a fixed common ratio r. To find a missing term, first confirm r using several consecutive pairs of the given terms, and then apply that same ratio to the last known term.

Checking the given series:

1. 2500 ÷ 5000 = 0.5

2. 1250 ÷ 2500 = 0.5

3. 625 ÷ 1250 = 0.5

4. 312.5 ÷ 625 = 0.5

5. The ratio is consistently 0.5, so the next term = 312.5 × 0.5 = 156.25

As a check, reversing the step gives 156.25 × 2 = 312.5, which matches the term just before it, confirming the ratio holds all the way to the missing term.

So, the missing term is 156.25.