Question

What is the next number in the series: 3, 8, 15, 24, 35, ?

• A. 48
• B. 47
• C. 49
• D. 50

Hint:

• Look for patterns in the differences between terms.
• Alternatively, try to find a formula that generates the terms, such as $n^2 \pm k$, $n^3 \pm k$, etc.
• Here, the differences increase by 2 each time (5, 7, 9, 11, ...). The next difference is 13.
• Or, the series can be seen as $n \times (n+2)$ for $n=1,2,3,4,5$: $1\times3=3, 2\times4=8, 3\times5=15, 4\times6=24, 5\times7=35$. Next term is $6\times8=48$.
• Or, as $(n+1)^2-1$ for $n=1,2,3,4,5$. Next term $n=6$: $(6+1)^2-1 = 7^2-1=48$.

Answer 1

The Correct Option is A

Examining the differences between consecutive terms of the series: $8 - 3 = 5$
$15 - 8 = 7$
$24 - 15 = 9$
$35 - 24 = 11$
The sequence of differences is 5, 7, 9, 11. This forms an arithmetic progression of odd numbers with a common difference of 2. The subsequent difference is predicted to be $11 + 2 = 13$. Therefore, the next number in the series is calculated as $35 + 13 = 48$.
Alternatively, the terms can be expressed by the formula $n^2 - 1$, where $n$ takes values from 2 to 6: For $n=2$: $2^2 - 1 = 4 - 1 = 3$
For $n=3$: $3^2 - 1 = 9 - 1 = 8$
For $n=4$: $4^2 - 1 = 16 - 1 = 15$
For $n=5$: $5^2 - 1 = 25 - 1 = 24$
For $n=6$: $6^2 - 1 = 36 - 1 = 35$
The subsequent term, for $n=7$, is determined by: For $n=7$: $7^2 - 1 = 49 - 1 = 48$. \[ \boxed{48} \]