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00:00 - 00:59 | Nohay in this question we have been given that a b c are in AP BC dr.ngp and 1.31.1 are in AP and B have to prove that a c are in GP ok now a b c are in AP so that means I can write this has to be request to a + b is there because of its ok now b c d are in GP I can write this is c square is equal to BD no since we have been given that these are in AP such that means I can read this to a point C is equals to 1 upon 3 + 1 upon basically we have to prove that these are in GP so that means we have to prove that AC square is equals to |

01:00 - 01:59 | latest use this equation ok so c square is equals to be in 2D now here I will be multiplying and dividing by two ok so this will be now if I take LCM of this so this will be in to let me right it again so this will be C plus ok now here you can see that too is equals to a + c and d by two will be if I take reciprocal of this month so this will be the white 2 is equals to see / C plus so I can write this too busy quotes to a + b into C / |

02:00 - 02:59 | ok now if I cross multiply so this will be so c square into C plus is this will be C cube plus c square he that is equals to Dosti into a + b + c square Nahar considered c square gets cancelled out and we get C cube in cube in cube is equal to AC ok now here you can see that this she gets cancelled out with this one by two statements E square is equals to E Cigarette means these are in GP ok so here we have |

03:00 - 03:59 | prove this one no according we have got this that means these are in ECE are in GP and this complete solution so that means ECE are in GP ok |

**Representation of sequences and different types of series**

**Definition + algorithm to determine the sequence of AP**

**General term of an AP**

**`n^(th)` term of an AP from the end**

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