The following series of numbers is given. One number is missing. Study the pattern and find the missing number. 8, 32, 72, 128, ?

Correct — B.
Rule: each term is 8 × n², so the gaps 24, 40, 56 grow by 16.

8 = 8 × 1²
32 = 8 × 2²
72 = 8 × 3²
128 = 8 × 4²

Next: 8 × 5² = 8 × 25 = 200 → option (b).
Check: the next gap is 56 + 16 = 72, and 128 + 72 = 200.

Why the others are wrong

• (a)
  228 — 228 ÷ 8 = 28.5, not a whole number, so it is not 8 times a square. It would also need a gap of 100 after 128, not 72.
• (c)
  250 — 250 ÷ 8 = 31.25, off the 8 × n² pattern. The gap would be 122, where the gaps 24, 40, 56 point to 72.
• (d)
  300 — 300 ÷ 8 = 37.5, off the pattern. It needs a jump of 172 from 128, more than double the 72 the gaps predict.

Two readings of this series agree, which makes a quick cross-check.

Divide by the first term: 8, 32, 72, 128 become 1, 4, 9, 16, the squares of 1 to 4. Take differences: 24, 40, 56 rise by a constant 16, and a constant second difference is the mark of a rule built on n². Either way the next term is 200.

Key facts

• 8, 32, 72, 128, 200 are 8 × 1², 8 × 2², 8 × 3², 8 × 4², 8 × 5².
• The gaps 24, 40, 56, 72 rise by 16 each time.
• Constant second differences point to a rule built on n².

Common traps

• Repeating the last gap instead of growing it: 128 + 56 = 184 is not even an option

No directly related past PYQ was found.