Number Series, Coding, Odd Man OutMTP Dec 22 - Series IQuestion 2062 of 217
All Questions

Find the missing term in each of the following series: 6,13,25,51,101.\displaystyle 6, 13, 25, 51, 101.

Options

A201\displaystyle 201
B205\displaystyle 205
C203\displaystyle 203
D207\displaystyle 207
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Correct Answer

✅ Option c — 203\displaystyle 203

All Options:

  • A201\displaystyle 201
  • B205\displaystyle 205
  • C203\displaystyle 203
  • D207\displaystyle 207

Detailed Solution & Explanation

To find the missing term of the series 6,13,25,51,101,?\displaystyle 6, 13, 25, 51, 101, ?, we analyze the relation between consecutive terms:

- 1st term to 2nd term: 6×2+1=13\displaystyle 6 \times 2 + 1 = 13
- 2nd term to 3rd term: 13×2−1=25\displaystyle 13 \times 2 - 1 = 25
- 3rd term to 4th term: 25×2+1=51\displaystyle 25 \times 2 + 1 = 51
- 4th term to 5th term: 51×2−1=101\displaystyle 51 \times 2 - 1 = 101

We observe an alternating pattern where each term is multiplied by 2\displaystyle 2 and then we alternately add 1\displaystyle 1 and subtract 1\displaystyle 1 (+1,−1,+1,−1,…\displaystyle +1, -1, +1, -1, \dots).
Following this pattern, the next term must be computed by multiplying the 5th term by 2\displaystyle 2 and adding 1\displaystyle 1:
101×2+1=202+1=203101 \times 2 + 1 = 202 + 1 = 203

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

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