Identify the Number Series

The given number series is: 240, ?, 120, 40, 10, 2.

The task is to find the missing term represented by the question mark.

Analyze the Pattern

Let's examine the relationship between the known terms, starting from the end of the series:

• The last term is 2.
• The term before that is 10. To get from 10 to 2, we divide by 5: $10 \div 5 = 2$.
• The term before 10 is 40. To get from 40 to 10, we divide by 4: $40 \div 4 = 10$.
• The term before 40 is 120. To get from 120 to 40, we divide by 3: $120 \div 3 = 40$.

The pattern observed is that each term is obtained by dividing the previous term by a decreasing sequence of integers: 5, 4, 3.

Determine the Missing Term

To continue this pattern, the divisors should be 2 and then 1.

• Let the missing term be $X$. The term 120 is obtained by dividing $X$ by 2. So, the calculation is $X \div 2 = 120$.
• The first term, 240, is obtained by dividing the missing term $X$ by 1. So, the calculation is $240 \div 1 = X$.

Now, we calculate the value of $X$ using the first term:

$X = 240 \div 1 = 240$.

Let's verify the complete series with $X = 240$:

• $240 \div 1 = 240$ (This is the missing term)
• $240 \div 2 = 120$ (Matches the next term)
• $120 \div 3 = 40$ (Matches)
• $40 \div 4 = 10$ (Matches)
• $10 \div 5 = 2$ (Matches)

The pattern $ \div 1, \div 2, \div 3, \div 4, \div 5 $ holds true.

Conclusion

The missing term in the series is 240.