Number Series, Coding, Odd Man OutMTP Sep 24 Series IIQuestion 2080 of 217
All Questions

Find next term of the series 1,3,4,8,15,27,?\displaystyle 1, 3, 4, 8, 15, 27, ?

Options

A37\displaystyle 37
B44\displaystyle 44
C50\displaystyle 50
D55\displaystyle 55
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Correct Answer

✅ Option c — 50\displaystyle 50

All Options:

  • A37\displaystyle 37
  • B44\displaystyle 44
  • C50\displaystyle 50
  • D55\displaystyle 55

Detailed Solution & Explanation

To find the next term of the series 1,3,4,8,15,27,?\displaystyle 1, 3, 4, 8, 15, 27, ?, let us analyze the relation of each term to its preceding terms:

We observe that starting from the fourth term (8\displaystyle 8), each term is the sum of the three preceding terms:
- 4th term: 1+3+4=8\displaystyle 1 + 3 + 4 = 8
- 5th term: 3+4+8=15\displaystyle 3 + 4 + 8 = 15
- 6th term: 4+8+15=27\displaystyle 4 + 8 + 15 = 27

This is the characteristic rule of a Tribonacci-like sequence:
Tn=Tn−1+Tn−2+Tn−3T_n = T_{n-1} + T_{n-2} + T_{n-3}
Following this logical progression, the next term (7th term) must be the sum of the 4th, 5th, and 6th terms:
- 7th term: 8+15+27=50\displaystyle 8 + 15 + 27 = 50

Therefore, the mathematically correct answer is **50\displaystyle 50**, which corresponds to **Option C**.

*Note on Answer Key Discrepancy:* The textbook answer key lists **Option D** (55\displaystyle 55) as the correct answer. However, 55\displaystyle 55 does not satisfy the clear, established Tribonacci progression of the sequence, whereas 50\displaystyle 50 completes the mathematical logic perfectly. This is a clear typographical error in the official answer key, and the correct option is **Option C**.

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

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