Question:
Find the missing number in the following number series: 266, 196, 256, 169, ___
Find the missing number in the following number series: 266, 196, 256, 169, ___
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Memorize squares up to 30 to spot patterns instantly.
Updated On: Jun 26, 2026
- 265
- 256
- 625
- 225
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Analyzing alternating series or patterns of squares.
Step 2: Analysis
The sequence includes squares of numbers: - $196 = 14^2$ - $256 = 16^2$ - $169 = 13^2$ Looking at the second, third, and fourth terms: $14^2$, $16^2$, $13^2$. This suggests two interleaved series.
Step 3: Pattern Identification
Alternating series 1: 266, 256, ? (Decreasing by 10) $\rightarrow$ $256 - 10 = 246$ (Not in options). Alternating series 2: 196, 169, ? ($14^2$, $13^2$...). Following the square pattern: $14^2$, $16^2$, $13^2$, $15^2$... The missing number is $15^2 = 225$.
Step 4: Conclusion
The next logical square in the sequence is 225. Final Answer: (4)
Analyzing alternating series or patterns of squares.
Step 2: Analysis
The sequence includes squares of numbers: - $196 = 14^2$ - $256 = 16^2$ - $169 = 13^2$ Looking at the second, third, and fourth terms: $14^2$, $16^2$, $13^2$. This suggests two interleaved series.
Step 3: Pattern Identification
Alternating series 1: 266, 256, ? (Decreasing by 10) $\rightarrow$ $256 - 10 = 246$ (Not in options). Alternating series 2: 196, 169, ? ($14^2$, $13^2$...). Following the square pattern: $14^2$, $16^2$, $13^2$, $15^2$... The missing number is $15^2 = 225$.
Step 4: Conclusion
The next logical square in the sequence is 225. Final Answer: (4)
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