What should come in place of ‘?’ in the given series? 149 161 178 200 227 ?
2026
What should come in place of ‘?’ in the given series?
149 161 178 200 227 ?
Answer: B. 259 — Concept: In a difference series (a second-order series), the terms themselves do not grow by a fixed amount; instead the gaps between consecutive terms form…
- A.
261
- B.
259
- C.
255
- D.
264
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Correct answer: B
Concept: In a difference series (a second-order series), the terms themselves do not grow by a fixed amount; instead the gaps between consecutive terms form their own arithmetic progression. The working rule follows from that: list the first differences, test whether those differences rise by a constant amount, then extend the difference pattern by one step and add that step to the last known term.
Application: Take the first differences of the printed terms 149, 161, 178, 200 and 227.
161 − 149 = 12
178 − 161 = 17
200 − 178 = 22
227 − 200 = 27
The differences 12, 17, 22, 27 each rise by 5, so the next difference is 27 + 5 = 32.
Missing term = 227 + 32 = 259.
Consecutive terms | Difference | Rise over the previous difference |
|---|---|---|
149 → 161 | 12 | — |
161 → 178 | 17 | 5 |
178 → 200 | 22 | 5 |
200 → 227 | 27 | 5 |
227 → 259 | 32 | 5 |
Cross-check: Rebuild the series forward from 149 using the steps 12, 17, 22, 27, 32: it gives 149, 161, 178, 200, 227, 259, reproducing every printed term. Comparing this against the values offered:
255 would force a last step of 28, a rise of only 1 over 27, breaking the constant rise.
261 would force a last step of 34, a rise of 7 over 27.
264 would force a last step of 37, a rise of 10 over 27.
259 keeps the rise at a constant 5, giving the step 32.
The missing term is 259.