What comes next in the following sequence? 0.25, 2.25, 6.25, 12.25, ?
2022
What comes next in the following sequence?
0.25, 2.25, 6.25, 12.25, ?
Answer: D. 20.25 — ConceptIn a sequence, first differences show how much each term changes from the preceding term. When those differences follow a simple pattern, extend that…
- A.
18.25
- B.
19.25
- C.
16.25
- D.
20.25
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Show answer & explanation
Correct answer: D
Concept
In a sequence, first differences show how much each term changes from the preceding term.
When those differences follow a simple pattern, extend that pattern and add the next difference to the last known term.
Application
Subtract consecutive terms: 2.25 - 0.25 = 2.
The next difference is 6.25 - 2.25 = 4.
The following difference is 12.25 - 6.25 = 6.
The differences are 2, 4, 6, so the next difference is 8.
Add this to the last term: 12.25 + 8 = 20.25.
Cross-check
The first differences increase by 2 each time: 2 to 4, 4 to 6, and 6 to 8. This confirms that the next term is 20.25.