The question presents a number sequence and asks for the next term.
Sequence Pattern Recognition
We need to identify the rule governing the sequence: 3, 6, 18, 72, 360, ?
Let's examine the relationship between consecutive terms:
- $6 \div 3 = 2$
- $18 \div 6 = 3$
- $72 \div 18 = 4$
- $360 \div 72 = 5$
The pattern is that each term is obtained by multiplying the previous term by an integer, starting from 2 and increasing by 1 for each subsequent step.
Calculating the Next Term
Following the identified pattern, the next operation is to multiply the last term (360) by the next integer in the sequence, which is 6.
- The sequence of multipliers is: 2, 3, 4, 5, ...
- The next multiplier is 6.
- Calculation: $360 \times 6$
Performing the multiplication:
$360 \times 6 = 2160$
Therefore, the next number in the sequence is 2160.
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Select the number from among the given options that can replace the question mark (?) in the following series.
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