Question

Select the related numbers from the given alternative
3, 9, 18, 16, 33, 23 (...)

• A. 48
• B. 51
• C. 54
• D. 58

Hint:

If a series goes up and down, it is almost always an interleaved series combining two separate sequences. Separate the alternate terms to identify the pattern easily.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Number series questions often contain multiple interleaved sub-series.
If the differences between consecutive terms alternate irregularly, check the values at alternate positions (even and odd positions) to find the pattern.

Step 2: Detailed Explanation:
Let us separate the given series into two alternate sub-series:
The given series is:
\[ 3, \; 9, \quad 18, \; 16, \quad 33, \; 23, \quad (\dots) \]
1. Sub-series 1 (Odd-indexed positions):
- First term: 3
- Third term: 18
- Fifth term: 33
Let us look at the differences between these terms:
\[ 18 - 3 = 15 \]
\[ 33 - 18 = 15 \]
This sub-series is an arithmetic progression with a constant common difference of \(+15\).
2. Sub-series 2 (Even-indexed positions):
- Second term: 9
- Fourth term: 16
- Sixth term: 23
Let us look at the differences between these terms:
\[ 16 - 9 = 7 \]
\[ 23 - 16 = 7 \]
This sub-series is an arithmetic progression with a constant common difference of \(+7\).
3. Determine the next term:
The next term in the main series (the 7th term) corresponds to the next term in Sub-series 1:
\[ \text{Next term} = 33 + 15 = 48 \]
This matches Option A.

Step 3: Final Answer:
The next number in the series is 48.