Number Series, Coding, Odd Man OutMTP June 24 Series IQuestion 2075 of 217
All Questions

Find out the next number in the following series 7,11,13,17,19,23,25,29,?\displaystyle 7, 11, 13, 17, 19, 23, 25, 29, ?

Options

A30\displaystyle 30
B31\displaystyle 31
C32\displaystyle 32
D33\displaystyle 33
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Correct Answer

✅ Option b — 31\displaystyle 31

All Options:

  • A30\displaystyle 30
  • B31\displaystyle 31
  • C32\displaystyle 32
  • D33\displaystyle 33

Detailed Solution & Explanation

To find the next number in the series 7,11,13,17,19,23,25,29,?\displaystyle 7, 11, 13, 17, 19, 23, 25, 29, ?, we can analyze the logical progression using two standard methods:

**Method 1: Alternating Differences (+4\displaystyle +4 and +2\displaystyle +2)**
Let us examine the difference between successive terms of the series:
- 11−7=+4\displaystyle 11 - 7 = +4
- 13−11=+2\displaystyle 13 - 11 = +2
- 17−13=+4\displaystyle 17 - 13 = +4
- 19−17=+2\displaystyle 19 - 17 = +2
- 23−19=+4\displaystyle 23 - 19 = +4
- 25−23=+2\displaystyle 25 - 23 = +2
- 29−25=+4\displaystyle 29 - 25 = +4
We observe a clear, repeating, alternating pattern of adding 4\displaystyle 4 and then adding 2\displaystyle 2 (+4,+2,+4,+2,…\displaystyle +4, +2, +4, +2, \dots).
Following this pattern, the next difference must be +2\displaystyle +2. We add 2\displaystyle 2 to the last term (29\displaystyle 29):
29+2=3129 + 2 = 31
**Method 2: Split Alternating Subseries**
We can divide the series into two independent subseries based on odd and even positions:

1. **Odd-position Subseries (1st, 3rd, 5th, 7th, 9th terms):**
- Terms: 7,13,19,25,?\displaystyle 7, 13, 19, 25, ?
- We observe a constant difference of +6\displaystyle +6 between consecutive terms (7+6=13\displaystyle 7+6=13, 13+6=19\displaystyle 13+6=19, 19+6=25\displaystyle 19+6=25).
- Following this constant +6\displaystyle +6 progression, the 9th term (the missing term) must be:
25+6=3125 + 6 = 31
2. **Even-position Subseries (2nd, 4th, 6th, 8th terms):**
- Terms: 11,17,23,29\displaystyle 11, 17, 23, 29
- We also observe a constant difference of +6\displaystyle +6 (11+6=17\displaystyle 11+6=17, 17+6=23\displaystyle 17+6=23, 23+6=29\displaystyle 23+6=29).

Both independent methods mathematically prove that the next term in the sequence is **31\displaystyle 31**, which corresponds to **Option B**.

*Note on Answer Key Discrepancy:* The textbook answer key lists **Option D** (33\displaystyle 33) as the correct option. However, 33\displaystyle 33 violates both the alternating difference pattern and the split-series progression, whereas 31\displaystyle 31 is logically and mathematically perfect. This is a clear typographical error in the official answer key, and the correct option is **Option B**.

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

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