Give an expression or formula for the number of squares \( (s) \) in the \( n \)th picture. INSTRUCTIONS: - The first part of the formula has been written for you. You must complete the formula in terms of \( n \). - You do not need to simplify the expression.

1. Recognize that in the first picture there is \( 1 \) square. 2. In each subsequent picture, additional squares are added. The pattern given is that the number of squares added at step \( k \) (for \( k = 1,\, 2,\, \dots,\, n-1 \)) is \( 4k \). 3. Therefore, the total number of squares \( s \) in the \( n \)th picture can be written as \[ s = 1 + \sum_{k=1}^{n-1} 4k. \] 4. Since the sum of the first \( n-1 \) positive integers is \[ \sum_{k=1}^{n-1} k = \frac{n(n-1)}{2}, \] we substitute to get \[ s = 1 + 4\left(\frac{n(n-1)}{2}\right). \] This is the required expression for the number of squares in the \( n \)th picture.