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

Question

Question

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

Answer 1

\(x + k(n-1)\)

Answer 2

## 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 \(n^{th}\) 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.

Question

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

Answer

Answer

Explain

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