What should come in place of the question mark (?) in the given series? 500,…

Concept: In this type of number series, the difference between consecutive terms does not stay constant — instead, each successive difference is exactly double the previous difference, forming a geometric progression of differences (common ratio 2).

Application:

1. Difference between the 1st and 2nd terms: 495 − 500 = −5.

2. Difference between the 2nd and 3rd terms: 485 − 495 = −10.

3. Difference between the 3rd and 4th terms: 465 − 485 = −20.

4. Difference between the 4th and 5th terms: 425 − 465 = −40.

5. Continuing the same doubling pattern, the next difference is −80.

6. Adding this difference to the 5th term: 425 + (−80) = 345.

Cross-check: Listing the full sequence of differences gives −5, −10, −20, −40, −80 — each term in this list is exactly double the one before it, confirming the pattern holds consistently across the whole series. So the missing term is 345.