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

Let's analyze the differences between consecutive terms in the series: $8 - 3 = 5$
$15 - 8 = 7$
$24 - 15 = 9$
$35 - 24 = 11$
The differences are 5, 7, 9, 11. This is an arithmetic progression of odd numbers, with a common difference of 2.
The next difference in this sequence should be $11 + 2 = 13$.
So, the next number in the series will be $35 + 13 = 48$.
Alternatively, the terms can be represented as $n^2 - 1$ for $n=2, 3, 4, 5, 6$: $2^2 - 1 = 4 - 1 = 3$
$3^2 - 1 = 9 - 1 = 8$
$4^2 - 1 = 16 - 1 = 15$
$5^2 - 1 = 25 - 1 = 24$
$6^2 - 1 = 36 - 1 = 35$
The next term would be for $n=7$:
$7^2 - 1 = 49 - 1 = 48$.
\[ \boxed{48} \]