# S-Cool Revision Summary

## S-Cool Revision Summary

## nth term

**nth term = dn + (a - d)**

where **d** is the difference and **a** is the first term.

If the second difference is constant (and first difference changes),

where **a** is the first term, **d** is the difference between the first and second terms and **c** is the **second difference**.

**Alternatively:**

- If the first difference keeps changing but the second difference is constant then the formula is something to do with '
**n**'. Make a table showing the first few terms of '^{2}**n**'.^{2} - In the next column of your table write the differences between the term of '
**n**' and your sequence.^{2} - Find the formula for
**this**new sequence using**dn + (a - d)** - Add it on to
**n**to give you your final formula^{2}

*Well-known sequences*

Sequence |
Name |
nth term |

2,4,6,8,... | Even numbers | 2n |

1,3,5,7,... | Odd numbers | 2n - 1 |

1,4,9,16,25,... | Square numbers | n^{2} |

1,8,27,64,125,... | Cube numbers | n^{3} |

1,3,6,10,15,... | Triange numbers | ½ n(n + 1) |

2,3,5,7,11,13,... | Prime numbers | Not known |

1,1,2,3,5,8,13,... | Fibonacci numbers | Not needed |