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# Equations are given below illustrating a suspected number pattern.

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+225

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.

1 = 1 X 1

1 + 9 = 2 X 5

1 + 9 + 17 = 3 X 9

Sep 6, 2017

#1
+1

1 = 1 X 1 True

1 + 9 = 2 X 5 True

1 + 9 + 17 = 3 X 9 True

1 + 9 + 17 + 25 = 4 x 13 True

1+ 9 + 17 + 25 + 33 = 5 x 17 True

1+ 9 + 17 + 25 + 33 + 41 = 6 x 21 True............etc.

Notice the pattern. The LHS forms an arithmetic sequence with a common difference of 8. The RHS forms a pattern of: 1, 2, 3, 4, 5.....etc., each is multiplied by the PREVIOUS multiplicand + 4. So you have: 1 x 1, 2 x (4 + 1),  3 x (4+5), 4 x (4 + 9), 5 x (4 + 13), 6 x (4 + 17).......etc.

Sep 6, 2017

#1
+1

1 = 1 X 1 True

1 + 9 = 2 X 5 True

1 + 9 + 17 = 3 X 9 True

1 + 9 + 17 + 25 = 4 x 13 True

1+ 9 + 17 + 25 + 33 = 5 x 17 True

1+ 9 + 17 + 25 + 33 + 41 = 6 x 21 True............etc.

Notice the pattern. The LHS forms an arithmetic sequence with a common difference of 8. The RHS forms a pattern of: 1, 2, 3, 4, 5.....etc., each is multiplied by the PREVIOUS multiplicand + 4. So you have: 1 x 1, 2 x (4 + 1),  3 x (4+5), 4 x (4 + 9), 5 x (4 + 13), 6 x (4 + 17).......etc.

Guest Sep 6, 2017