A matchstick pattern uses 4 sticks for 1 square, 7 sticks for 2 squares joined in a row, and 10 sticks for 3 squares. Write a rule for the number of sticks needed to make n squares.
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Step-by-Step Solution
Step 1: Identify the pattern
First, we observe the given information to identify the number of matchsticks required for 1, 2, and 3 squares. This helps us to see the sequence of numbers involved.
Step 2: Find the common difference
We calculate the difference between the number of sticks for consecutive squares. Since the difference is constant, this indicates an arithmetic progression.
Step 3: Apply the arithmetic progression formula
We use the formula for the n -th term of an arithmetic progression, where an is the number of sticks for n squares, a1 is the number of sticks for the first square, and d is the common difference.
Step 4: Substitute values and simplify
Substitute the first term a1=4 and the common difference d=3 into the formula. Then, simplify the expression to get the rule for n squares.