Determine the missing number in the given sequence.

15, 24, 35, 48, ?

The correct option is 63.

Step-by-step Explanation:

To find the missing number in the sequence 15, 24, 35, 48, ?, we can analyze the pattern of differences between consecutive terms or express each term as a mathematical function of its position.

Method 1: Difference between consecutive terms

Let's calculate the difference between each adjacent pair of numbers in the sequence:

$24-15=9$

$35-24=11$

$48-35=13$

Notice that the differences between consecutive terms ($9,11,13$) increase by $2$ each time. These differences form a sequence of consecutive odd numbers.

Following this pattern, the next difference to add to $48$ is $13+2=15$.

Therefore, the missing term is:

$48+15=63$

Method 2: Pattern of squares ($n^2-1$)

Each term in the sequence can also be represented as $n^2-1$, starting with $n=4$:

$4^2-1=16-1=15$

$5^2-1=25-1=24$

$6^2-1=36-1=35$

$7^2-1=49-1=48$

For the missing 5th term ($n=8$):

$8^2-1=64-1=63$

Hence, the missing number in the given sequence is 63.