Series 6, 24, 60, 120, ? What number will come at the place of the ?

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Question: What number will come at the place of the question mark (?) in the series 6, 24, 60, 120 ?

Series: 6, 24, 60, 120, ?

Options:

1. 150
2. 180
3. 210
4. 135

Solution:

This is a number series where a specific pattern exists between the numbers. To solve this, we need to figure out how each number is generated.

The first four numbers in the series are:

• 6, 24, 60, 120

Now, let’s analyze the pattern by expressing these numbers in a particular mathematical form:

• 6 can be written as (1 \times 2 \times 3)
• 24 can be written as (2 \times 3 \times 4)
• 60 can be written as (3 \times 4 \times 5)
• 120 can be written as (4 \times 5 \times 6)

Now, we can see that each number follows the form (n(n+1)(n+2)), where (n) starts at 1 and increases by 1 in each step.

For the next number, (n = 5), so:

• (5 \times 6 \times 7 = 210)

Thus, the next number in the series is 210.

Answer:

The correct answer is: 3. 210

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