In the following question, a number series is given with one term missing.…
2023
In the following question, a number series is given with one term missing. Choose the correct alternative that follows the same pattern and completes the series: 1, 4, 9, 16, 25, ?
- A.
35
- B.
36
- C.
48
- D.
49
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept: A number series problem asks you to identify the rule that generates each term from its position in the sequence, then apply that same rule to find the missing term. Common rules include a constant difference, a constant ratio, or squares/cubes of consecutive integers.
Application:
Write each given term as the square of its position: 1 = 12, 4 = 22, 9 = 32, 16 = 42, 25 = 52.
The position number matches the term's rank, so the governing rule is: nth term = n2.
The missing term is the 6th term, so apply the rule: 62 = 36.
Cross-check: The differences between consecutive terms are 4-1=3, 9-4=5, 16-9=7, 25-16=9 - an increasing sequence of odd numbers, each 2 more than the last. Continuing this pattern, the next difference is 11, so 25 + 11 = 36, matching the squares rule.
Both methods confirm the missing term is 36.