Number Series Reasoning

The question asks to identify the missing number in the given series: 4, 8, 24, 96, ?, 2880.

Series Pattern Analysis

To find the missing term, we need to determine the pattern governing the series.

• Compare the first two terms: $8 / 4 = 2$. The first term is multiplied by 2 to get the second term ($4 \times 2 = 8$).
• Compare the second and third terms: $24 / 8 = 3$. The second term is multiplied by 3 to get the third term ($8 \times 3 = 24$).
• Compare the third and fourth terms: $96 / 24 = 4$. The third term is multiplied by 4 to get the fourth term ($24 \times 4 = 96$).

The pattern observed is that each term is multiplied by consecutive integers (2, 3, 4, ...) to obtain the next term.

Calculating the Missing Term

Following the established pattern:

• The next multiplier should be 5. Multiply the fourth term (96) by 5: $96 \times 5 = 480$.
• The term following the missing one should be obtained by multiplying 480 by the next integer, 6. Let's check: $480 \times 6 = 2880$.

This confirms the pattern. The missing term in the series is 480.

Therefore, the series is: $4 \xrightarrow{\times 2} 8 \xrightarrow{\times 3} 24 \xrightarrow{\times 4} 96 \xrightarrow{\times 5} 480 \xrightarrow{\times 6} 2880$.