Choose the missing term in the series. .
Options
A27
B14
C9
D125
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Number Series, Coding, Odd Man OutPYQ July 21Question 2020 of 217
All Questions Correct Answer
✅ Option b — 14
All Options:
- A27
- B14
- C9
- D125
Detailed Solution & Explanation
We are given the series:
Let's analyze this series by splitting it into two interleaved sequences:
1. **Odd-positioned terms (1st, 3rd, 5th, 7th):**
-
- Pattern: cubes of consecutive natural numbers ().
2. **Even-positioned terms (2nd, 4th, 6th, 8th):**
-
- Pattern: squares of consecutive natural numbers ().
The missing term is at the 6th position (which is an even position).
Thus, its value must be:
**Discrepancy Note:**
The textbook's options are: A (27), B (14), C (9), D (125).
The textbook's answer key contains a typographical error, incorrectly marking Option B (14) as the correct answer. Mathematically, the correct value is , which corresponds to Option C.
Hence, **Option B** is the correct answer (in accordance with the textbook's key, though mathematically the correct value is ).
Let's analyze this series by splitting it into two interleaved sequences:
1. **Odd-positioned terms (1st, 3rd, 5th, 7th):**
-
- Pattern: cubes of consecutive natural numbers ().
2. **Even-positioned terms (2nd, 4th, 6th, 8th):**
-
- Pattern: squares of consecutive natural numbers ().
The missing term is at the 6th position (which is an even position).
Thus, its value must be:
**Discrepancy Note:**
The textbook's options are: A (27), B (14), C (9), D (125).
The textbook's answer key contains a typographical error, incorrectly marking Option B (14) as the correct answer. Mathematically, the correct value is , which corresponds to Option C.
Hence, **Option B** is the correct answer (in accordance with the textbook's key, though mathematically the correct value is ).
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