Find out the next number in the following series $7, 11, 13, 17, 19, 23, 25, 29, ?$
Select Your Answer (Keyboard: A, B, C, D)
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Number Series, Coding and DecodingMCQMTP June 24 Series IQuestion 2075 of 217
All Questions Correct Answer
✅ Option b — $31$
All Options:
- A$30$
- B$31$
- C$32$
- D$33$
Detailed Solution & Explanation
To find the next number in the series $7, 11, 13, 17, 19, 23, 25, 29, ?+4+2\displaystyle )**<br>Let us examine the difference between successive terms of the series:<br>- $11 - 7 = +4
- $13 - 11 = +2\displaystyle <br>- $17 - 13 = +4
- $19 - 17 = +2\displaystyle <br>- $23 - 19 = +4
- $25 - 23 = +2\displaystyle <br>- $29 - 25 = +4
We observe a clear, repeating, alternating pattern of adding and then adding ().
Following this pattern, the next difference must be . We add to the last term ($29\displaystyle ):<br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>29</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>31</mn></mrow><annotation encoding="application/x-tex">29 + 2 = 31</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">31</span></span></span></span></span><br>**Method 2: Split Alternating Subseries**<br>We can divide the series into two independent subseries based on odd and even positions:<br><br>1. **Odd-position Subseries (1st, 3rd, 5th, 7th, 9th terms):**<br>- Terms: $7, 13, 19, 25, ?
- We observe a constant difference of between consecutive terms (, $13+6=19\displaystyle , $19+6=25).
- Following this constant progression, the 9th term (the missing term) must be:
2. **Even-position Subseries (2nd, 4th, 6th, 8th terms):**
- Terms: $11, 17, 23, 29+6\displaystyle ($11+6=17, $17+6=23\displaystyle , $23+6=29).
Both independent methods mathematically prove that the next term in the sequence is **$31\displaystyle **, which corresponds to **Option B**.<br><br>*Note on Answer Key Discrepancy:* The textbook answer key lists **Option D** ($33) as the correct option. However, $33\displaystyle violates both the alternating difference pattern and the split-series progression, whereas $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.
- $13 - 11 = +2\displaystyle <br>- $17 - 13 = +4
- $19 - 17 = +2\displaystyle <br>- $23 - 19 = +4
- $25 - 23 = +2\displaystyle <br>- $29 - 25 = +4
We observe a clear, repeating, alternating pattern of adding and then adding ().
Following this pattern, the next difference must be . We add to the last term ($29\displaystyle ):<br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>29</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>31</mn></mrow><annotation encoding="application/x-tex">29 + 2 = 31</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">31</span></span></span></span></span><br>**Method 2: Split Alternating Subseries**<br>We can divide the series into two independent subseries based on odd and even positions:<br><br>1. **Odd-position Subseries (1st, 3rd, 5th, 7th, 9th terms):**<br>- Terms: $7, 13, 19, 25, ?
- We observe a constant difference of between consecutive terms (, $13+6=19\displaystyle , $19+6=25).
- Following this constant progression, the 9th term (the missing term) must be:
2. **Even-position Subseries (2nd, 4th, 6th, 8th terms):**
- Terms: $11, 17, 23, 29+6\displaystyle ($11+6=17, $17+6=23\displaystyle , $23+6=29).
Both independent methods mathematically prove that the next term in the sequence is **$31\displaystyle **, which corresponds to **Option B**.<br><br>*Note on Answer Key Discrepancy:* The textbook answer key lists **Option D** ($33) as the correct option. However, $33\displaystyle violates both the alternating difference pattern and the split-series progression, whereas $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.
About This Chapter: Number Series, Coding and Decoding
Paper
Paper 3: Quantitative Aptitude
Weightage
5 Marks
Key Topics
Number series, Coding & Decoding, Odd man out
This chapter covers Number series, Coding & Decoding, Odd man out and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.
View Official ICAI SyllabusExam Strategy Tip
This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.
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