Difficulty: Medium
Correct Answer: 1440
Explanation:
Introduction / Context:
This number series grows rapidly by multiplication with a changing multiplier. The learner must identify how each term is obtained from the previous term by using progressively smaller integer factors. Such patterns often appear in competitive exam series questions to test observation and multiplication skills.
Given Data / Assumptions:
- Series: 12, 60, 240, 720, ?
- One term is missing in the fifth position.
- The terms increase significantly, suggesting multiplication.
Concept / Approach:
To solve, compute the ratio between consecutive terms and inspect how this ratio changes. Here, the series seems to multiply by 5, then 4, then 3, and then likely by 2. This descending multiplier pattern is common and leads directly to the missing term.
Step-by-Step Solution:
Step 1: Compute ratios between consecutive terms.
60 ÷ 12 = 5.
240 ÷ 60 = 4.
720 ÷ 240 = 3.
Step 2: The multipliers are 5, 4, and 3, decreasing by 1 each time.
Step 3: The next logical multiplier is 2.
Step 4: Multiply 720 by 2 to get the missing term: 720 * 2 = 1440.
Verification / Alternative check:
Rebuild the pattern from the start: 12 * 5 = 60, 60 * 4 = 240, 240 * 3 = 720, 720 * 2 = 1440. This confirms the descending sequence of multipliers and verifies that 1440 is correct.
Why Other Options Are Wrong:
- Option 1420 does not equal 720 multiplied by any neat integer that fits the pattern.
- Option 1400 also fails the simple multiplier rule and would break the systematic sequence.
- Option 1460 is similarly inconsistent with the neat multiplication pattern.
Common Pitfalls:
Learners may try to treat the growth as a fixed ratio or may miscalculate one of the products. Another error is to ignore the clear pattern in the multipliers and guess a value that seems close but does not actually follow the rule. Confirming ratios carefully prevents such mistakes.
Final Answer:
The missing term in the series is 1440, so the correct option is 1440.
Discussion & Comments