Question

What comes next?
3, 12, 27, 48, 75, 108, ?

• A. 147
• B. 162
• C. 183
• D. 192

Answer 1

The Correct Option is A

To determine the next number in the series 3, 12, 27, 48, 75, 108, we look for a pattern based on the given numbers.

The pattern appears to be a sequence of cubes with a linear adjustment. Let's break it down step by step:

1. Calculate the difference between consecutive terms to detect any pattern. 

Term Position	Value	Difference
1	3	-
2	12	12 - 3 = 9
3	27	27 - 12 = 15
4	48	48 - 27 = 21
5	75	75 - 48 = 27
6	108	108 - 75 = 33

1. Notice the differences: 9, 15, 21, 27, 33.
2. The difference between consecutive differences is constant:
   • 15 - 9 = 6
   • 21 - 15 = 6
   • 27 - 21 = 6
   • 33 - 27 = 6
3. This indicates the differences are an arithmetic sequence with a common difference of 6.
4. Predict the next difference:
   • The next difference should be 33 + 6 = 39.
5. Calculate the next term in the original sequence:
   • The next term after 108 should be 108 + 39 = 147.

Thus, the next number in the series is 147.

This logic confirms that the correct option is 147.