# Count On

## Explorer

#### Powerful Number Patterns

Here are some number patterns all involving the sum of neighbouring numbers
(consecutive numbers). Can you spot the patterns here? Hint: why are they
called *powerful* number patterns?

1 | = ? |

1+2+1 | = ? |

1+2+3+2+1 | = ? |

1+2+3+4+3+2+1 | = ? |

1+2+3+4+5+4+3+2+1 | = ? |

1+2+3+4+5+6+5+4+3+2+1 | = ? |

... | ... |

The second number pattern goes in pairs, where the second of each pair extends the first in the pair: so, for example, 2+3+4 is the first of a pair and the second extends it to 2+3+4+5+6+7.

1 1+2 | = ? = ? |

2+3+4 2+3+4+5+6+7 | = ? = ? |

5+6+7+8+9+10+11+12+13 5+6+7+8+9+..+20+21+22 | = ? = ? |

14+15+...+39+40 14+15+...+? | = ? = ? |