Step 1: Understanding the Concept:
This series involves percentage-based changes or consistent fractional increases and decreases. Step 2: Identifying the Vector of Change:
- $10000$ to $11000$: Increase of 10% ($+1000$).
- $11000$ to $9900$: Decrease of 10% ($-1100$).
- $9900$ to $10890$: Increase of 10% ($+990$).
- $10890$ to $9801$: Decrease of 10% ($-1089$). Step 3: Calculation:
The pattern is $+10%$ then $-10%$. The last operation was $-10%$, so the next must be $+10%$:
$9801 + 980.1 = 10781.1$.
Rounding to the nearest whole number gives 10781. Step 4: Final Answer:
The next number in the series is 10781. Thus, the correct option is (a).