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# Equations are given below illustrating a suspected number pattern.

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Equations are given below illustrating a suspected number pattern. Determine what the next equation would be, and verify that it is indeed a true statement.

2 = 1 X 2

2 + 6 = 2 X 4

2 + 6 + 10 = 3 X 6

A. The next equation is. It is a true statement because both the left and right sides of the equation simplify to

B. The next equation is. It is a false statement because the left side of the equation simplifies to and the right side of the equation simplifies to

Sep 6, 2017
edited by cassie19  Sep 6, 2017

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2 = 1 X 2 True

2 + 6 = 2 X 4 True

2 + 6 + 10 = 3 X 6 True

2 + 6 + 10 + 14 = 4 x 8 True

2 + 6 + 10 + 14 + 18 = 5 x 10 True

2 + 6 + 10 + 14 + 18 + 22 = 6 x 12 True

2 + 6 + 10 + 14 + 18 + 22 + 26 = 7 x 14 True............etc.

Notice the pattern. The LHS is an arithmetic sequence with a common difference of 4. The RHS forms a pattern of 1, 2, 3, 4, 5........ each multiplied by its double. 1 x 2, 2 x 4, 3 x 6, 4 x 8, 5 x 10......etc.

Sep 6, 2017