Select the number from the given options to complete the series. 32, 36, 44, 56, 72, ___

Correct — B. Rule: the gaps run +4, +8, +12, +16 — each gap is 4 bigger than the one before it.

36 − 32 = 4
44 − 36 = 8
56 − 44 = 12
72 − 56 = 16

So the next gap is +20.

72 + 20 = 92 → option (b).

Why the others are wrong

• (a)
  98 — 98 needs a jump of +26 from 72. The gaps climb by a fixed 4 each time — 4, 8, 12, 16 — so the one after 16 is 20, not 26.
• (c)
  80 — 80 is 72 + 8, and a gap of 8 has already been used once, between 36 and 44. No gap repeats here.
• (d)
  90 — 90 is 72 + 18. That would mean the gap grew by only 2 after 16, while every earlier step grows by 4.

Read this series through its differences, not through the terms themselves. Write the gaps in a row underneath the series and look at that row the way you looked at the original numbers.

Here the gaps are 4, 8, 12, 16 — themselves an arithmetic progression with common difference 4. When the first differences form an AP, the series is quadratic: the terms accelerate while the gaps grow steadily.

If the gaps are not obvious, take their differences too. A second row that comes out constant tells you the pattern is complete and you can stop looking.

Key facts

• The gaps of 32, 36, 44, 56, 72 are 4, 8, 12, 16 — an AP with common difference 4.
• The next gap is 20, giving 72 + 20 = 92.
• The nth term is 2n² − 2n + 32, which returns 32, 36, 44, 56, 72, 92.

Common traps

• Adding the last gap again (72 + 16 = 88) instead of increasing it.
• Reading 4, 8, 12, 16 as a doubling pattern rather than as +4 each time.
• Checking the rule on the first two gaps only and then choosing.

No directly related past PYQ was found.