Completing the Number Series: 3, 6, 12, 24, ?, 96

This question asks us to identify the pattern in a given sequence of numbers and find the missing term. The sequence provided is $3, \ 6, \ 12, \ 24, \ ?, \ 96$.

Identifying the Pattern

Let's examine the relationship between consecutive numbers in the series:

• The first term is 3.
• The second term is 6. The relationship between the first and second term is $3 \times 2 = 6$.
• The third term is 12. The relationship between the second and third term is $6 \times 2 = 12$.
• The fourth term is 24. The relationship between the third and fourth term is $12 \times 2 = 24$.

It appears that each number in the series is obtained by multiplying the previous number by 2. This is a geometric progression with a common ratio of 2.

Calculating the Missing Term

To find the missing fifth term, we apply the same pattern:

Missing Term = Previous Term $\times$ 2

Missing Term = $24 \times 2$

Missing Term = $48$

Verifying the Pattern

Let's check if this pattern holds for the next term. The term after the missing number is 96.

Next Term = Missing Term $\times$ 2

Next Term = $48 \times 2$

Next Term = $96$

The calculated value matches the last term in the series, confirming that the pattern is correct.

The Completed Series

The completed series is $3, \ 6, \ 12, \ 24, \ 48, \ 96$.

Answer Options Analysis

The options provided are:

• 48
• 40
• 45
• 36

Based on our calculation, the missing number is 48.