Sam makes a sequence of patterns using tiles He adds the same number of tiles each time. Write an expression for the number of tiles in the n^th pattern. Tiles in nth patte rn: square

## Step1: First, we should note the progression of the sequence pattern that is described. ## Step2: Since it is mentioned that Sam adds the same number of tiles each time to the pattern, we could realize that this scenario represents an arithmetic sequence.## Step3: Let's represent the number of tiles added at each step as this constant k. Thus, from the first pattern to the pattern, there are exactly (n-1) 'steps' with each step incrementing the tile count by k.## Step4:So if our first pattern has x tiles, our nth pattern will have exactly:### \(x + k(n-1)\)tiles in it.