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The only way I can figure this out is by listing them all out one by one, which is TERRIBLE

Thank you so much in advance!!!!!

- Thread starter marsman
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- Thread starter
- #1

The only way I can figure this out is by listing them all out one by one, which is TERRIBLE

Thank you so much in advance!!!!!

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- Feb 7, 2012

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Suggestion: In the six figures, count how many toothpicks you have to add to each figure in order to get the next one. Can you see a pattern there?Please help! I need to be able to find the number of total toothpicks used in any given figure in this sequence, in addition to total squares in any figure, using the figure number.View attachment 1592

The only way I can figure this out is by listing them all out one by one, which is TERRIBLE

Thank you so much in advance!!!!!

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Yeah I'm up to my neck in patterns; I made a table and everything.Suggestion: In the six figures, count how many toothpicks you have to add to each figure in order to get the next one. Can you see a pattern there?

Figure Number | 1 | 2 | 3 | 4 | 5 |

Number of Toothpicks | 4 | 10 | 18 | 28 | 40 |

Increase in Toothpicks | +4 | +6 | +8 | +10 | +12 |

Number of Squares | 1 | 3 | 6 | 10 | 15 |

Increase in Squares | +1 | +2 | +3 | +4 | +5 |

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- Feb 7, 2012

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Let $x_n$ be the number of toothpicks in Fig. $n$. Your table shows that $x_1=4$, $x_2=4+6$, $x_3=4+6+8$, $x_4=4+6+8+10$, $\ldots$. So what is the formula for $x_n$?Yeah I'm up to my neck in patterns; I made a table and everything.

My problem is that I can't get from the patterns to creating a formula that would work for any figure number without listing them all out consecutively

Figure Number 1 2 3 4 5 Number of Toothpicks 4 10 18 28 40 Increase in Toothpicks +4 +6 +8 +10 +12 Number of Squares 1 3 6 10 15 Increase in Squares +1 +2 +3 +4 +5

Hints: arithmetic progression, $n$ terms, first term $4$, common difference $2$.