Question

Find the missing term in the following number series: 3, 10, 101, ?

• A. 10101
• B. 10201
• C. 10202
• D. 10102

Hint:

Look for patterns in the sequence, such as multiplication or addition with increasing terms.

Answer 1

The Correct Option is C

Let’s examine the given series: \[ 3, 10, 101, ? \] **Identify the pattern:** Start with 3.
The next term is obtained by concatenating the previous term with itself: \( 3 \) becomes \( 33 \), but this doesn't match the given series.
Alternatively, consider the following pattern:
\( 3 \times 3 + 1 = 10 \)
\( 10 \times 10 + 1 = 101 \)
\( 101 \times 101 + 1 = 10202 \)
**Verify the pattern:** \begin{itemize} \item \( 3 \times 3 + 1 = 10 \) \item \( 10 \times 10 + 1 = 101 \) \item \( 101 \times 101 + 1 = 10202 \) \end{itemize} **Determine the missing term:** \[ 101 \times 101 + 1 = 10202 \] **Final Answer:** \[ \boxed{10202} \] Therefore, the correct option is C) 10202.