Subject: Help the Helper!

Date: Sun, 20 Sep 1998 10:50:28 -0400

I am TRYING to help my niece with her Community College Teacher's math course! I have a BS and an Engineer yet stumble on what her book is asking:

- Fill in the blanks to continue this sequence of equations:
1 = 0+1 1+3+1 = 1+4 1+3+5+3+1 = 4+9 _______________ = ____ _______________ = ____ - What expression, suggested by part (1.), should be placed in the blank to complete this equation?
1 + 3 + 5.........+ (2n-3) + (2n-1)+ (2n-3)+...+5 + 3+ 1 = _________

John, Thanks

Hi John,

I think they are trying to have the students see a pattern.

If you complete two more rows you get

1 | = | 0+1 |

1+3+1 | = | 1+4 |

1+3+5+3+1 | = | 4+9 |

1+3+5+7+5+3+1 | = | 9+16 |

1+3+5+7+9+7+5+3+1 | = | 16+25 |

Now look at the last equation

1+3+5+7+9+7+5+3+1 = 16+25 (= 4^2 + 5^2).

This is a particular instance of the general expression in 2. with the middle term on the left equal to 9, that is 2n-1 = 9 so n = 5. You should now be able to guess the expression to place in the blank for part 2.

Cheers

Penny

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