Number Series, Coding, Odd Man OutMTP June 2023 Series IQuestion 2068 of 217
All Questions

Find the missing number in the following series? 2,15,10,17,26?\displaystyle 2, 15, 10, 17, 26?

Options

A49\displaystyle 49
B47\displaystyle 47
C37\displaystyle 37
D36\displaystyle 36
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Correct Answer

✅ Option c — 37\displaystyle 37

All Options:

  • A49\displaystyle 49
  • B47\displaystyle 47
  • C37\displaystyle 37
  • D36\displaystyle 36

Detailed Solution & Explanation

To solve the missing term of the series 2,15,10,17,26,?\displaystyle 2, 15, 10, 17, 26, ?, we must identify a significant typographical error in the sequence as printed in the textbook/MTP:

The second term, **15**, is a typographical error for **5**.

With this correction, the series becomes:
2,5,10,17,26,?2, 5, 10, 17, 26, ?
Let us analyze the logical pattern using two methods:

**Method 1: Quadratic Sequence (n2+1\displaystyle n^2 + 1)**
Each term Tn\displaystyle T_n represents n2+1\displaystyle n^2 + 1 starting from n=1\displaystyle n=1:
- T1=12+1=2\displaystyle T_1 = 1^2 + 1 = 2
- T2=22+1=5\displaystyle T_2 = 2^2 + 1 = 5 (erroneously printed as 15\displaystyle 15 in the question)
- T3=32+1=10\displaystyle T_3 = 3^2 + 1 = 10
- T4=42+1=17\displaystyle T_4 = 4^2 + 1 = 17
- T5=52+1=26\displaystyle T_5 = 5^2 + 1 = 26
- T6=62+1=37\displaystyle T_6 = 6^2 + 1 = 37

**Method 2: Difference Progression (Consecutive Odd Numbers)**
Let us look at the differences between successive terms of the corrected series:
- T2−T1=5−2=+3\displaystyle T_2 - T_1 = 5 - 2 = +3
- T3−T2=10−5=+5\displaystyle T_3 - T_2 = 10 - 5 = +5
- T4−T3=17−10=+7\displaystyle T_4 - T_3 = 17 - 10 = +7
- T5−T4=26−17=+9\displaystyle T_5 - T_4 = 26 - 17 = +9
The differences are consecutive odd numbers (3,5,7,9\displaystyle 3, 5, 7, 9). Therefore, the next difference must be +11\displaystyle +11:
T6=26+11=37T_6 = 26 + 11 = 37

Both methods prove that the next term in the series is **37\displaystyle 37**, which corresponds to **Option C**.

*Note on Answer Key Discrepancy:* The official answer key lists **Option D** (36\displaystyle 36) as correct. This is a double error: first, the typo of 15\displaystyle 15 instead of 5\displaystyle 5 in the question, and second, the selection of 36\displaystyle 36 (likely by calculating 62\displaystyle 6^2 and forgetting to add 1\displaystyle 1 to maintain the +1\displaystyle +1 offset). Mathematically and logically, the correct answer is **Option C** (37\displaystyle 37).

Hence, **Option C** is the correct answer.

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