**Hello Friends!**

Under this post "

**Number System: Arithmetic Progression and Geometric Progression**" we will see arithmetic progression and geometric progression, formula used for AP and GP and types of questions asked in competitive exams.

**1) Geometric Progression / Geometric Series / Geometric Sequence :**x, xr, xr

^{2}, xr

^{3}, xr

^{4}, --- are said to be in geometric progression. Here, a is first term and r is common ratio.

a) n

^{th}term = xr

^{ (n -1)}

b) Sum of n terms = | x (1 – r^{n}) | , here r < 1 |

(1 – r) |

c) Sum of n terms = | x (r^{n} – 1) | , here r > 1 |

(r – 1) |

**2) Arithmetic Progression / Arithmetic Series / Arithmetic Sequence :**x, x + y, x + 2y, x + 3y are said to be in A.P. Here x is first term and common difference is y.

a) n

^{th}term = x + (n – 1) y

b) Sum of n terms = | n | [2x + (n – 1)y] |

2 |

3) 1 + 2 + 3 +- - - - + n = | n(n + 1) |

2 |

4) (1^{2} + 2^{2} + 3^{2} - - - - + n^{2}) = | n(n + 1) (2n + 1) |

6 |

5) (1^{3} + 2^{3} + 3^{3} - - - - + n^{3}) = | n(n + 1) | ^{2} | ||

2 |

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