Select the number from among the given options that can replace the question mark (?) in the following series. 3, 20, 121, 604, 2417, ?

Correct — C. Rule: × 7 − 1, × 6 + 1, × 5 − 1, × 4 + 1, × 3 − 1 — the multiplier drops by one each step and the constant alternates minus and plus.

3 × 7 − 1 = 20
20 × 6 + 1 = 121
121 × 5 − 1 = 604
604 × 4 + 1 = 2417

The next step multiplies by 3 and subtracts:
2417 × 3 − 1 = 7250, which is option (c).

Why the others are wrong

• (a)
  7300 — 7300 is a rounded guess. The exact product is 2417 × 3 = 7251, and the step then subtracts one, so no value anywhere near 7300 is reachable.
• (b)
  7275 — 7275 sits above 2417 × 3 = 7251. The final step is × 3 − 1, and the alternation demands a minus here because the previous step added, so the answer must land just below 7251.
• (d)
  7200 — 7200 comes from multiplying a rounded 2400 by 3. Use the real term: 2417 × 3 = 7251, less 1 is 7250.

When the gaps between terms explode — 17, 101, 483, 1813 — stop taking differences and take ratios instead.

3 to 20 is roughly × 7, 20 to 121 roughly × 6, 121 to 604 roughly × 5. A multiplier stepping down by one is a standard SSC design.

Once the multipliers are visible the leftovers are tiny: minus 1, plus 1, minus 1, plus 1. Two patterns run at once, one on the multiplier and one on the constant, and you need both to reach the next term.

Key facts

• The series 3, 20, 121, 604, 2417 runs on × 7 − 1, then × 6 + 1, then × 5 − 1, then × 4 + 1.
• The next step is × 3 − 1, giving 2417 × 3 − 1 = 7250.
• When consecutive differences grow far faster than the terms themselves, test ratios before differences.

Common traps

• Taking first differences on a fast-growing series and losing a minute before switching to ratios
• Getting the multipliers right and forgetting that the constant alternates sign
• Rounding 2417 to 2400 and picking whichever option is nearest the estimate

No directly related past PYQ was found.