The first 15 numbers of a number pattern are given below. $9, 0, 8, 6, 9, 0, 8, 6, 9, 0, 8, 6, 9, 0, 8, \dots$
$\text{1}^{\text{st}} \hspace{6.5cm} \text{15}^{\text{th}}$ What is the $274^{\text{th}}$ number?

1. Identify the repeating sequence and its length.

The pattern is $9, 0, 8, 6$, which repeats every $4$ numbers.

2. Divide the target position by the length of the repeating sequence to find the remainder.

$274 \div 4 = 68$ with a remainder of $2$.

3. Determine the number at the target position based on the remainder.

A remainder of $2$ means the $274^{\text{th}}$ number is the $2^{\text{nd}}$ number in the repeating sequence, which is $0$.