Option 1)
would be the predicted next line in the pattern based on inductive reasoning.
Let's analyze the given pattern:
![\[ 3367 * 3 = 10,101 \]](https://img.qammunity.org/2024/formulas/mathematics/college/axit7bzb6rn31gaauw3lll85z3zc7vyzm9.png)
![\[ 3367 * 6 = 20,202 \]](https://img.qammunity.org/2024/formulas/mathematics/college/961vz2sy0oei4mndvgopvqdxpe9u13f56l.png)
![\[ 3367 * 9 = 30,303 \]](https://img.qammunity.org/2024/formulas/mathematics/college/k1pzgvobn699ps2ir2gh3blebsgqofvmrp.png)
![\[ 3367 * 12 = 40,404 \]](https://img.qammunity.org/2024/formulas/mathematics/college/8g1kufaagklxjj5p7c0xns8lyu208rqtgk.png)
The pattern appears to increase by 10,101 each time, suggesting a consistent multiplication of 3. If we continue this pattern:
![\[ 3367 * 15 = 50,505 \]](https://img.qammunity.org/2024/formulas/mathematics/college/gv62v9pfiodddw25080olibmrvuo39xava.png)
So, option 1)
would be the predicted next line in the pattern based on inductive reasoning.