Class 11 Maths Sequences Series | Geometric Progression |

**Geometric Progression**

Let’s suppose a student is asked to double the number of maths question practice every month. First month he practiced 50 questions. Number of questions he practiced over next few months will be 50, 100, 200, 400, 800 …

There is a pattern in this sequence; here if you divide any two consecutive numbers you will get same value. 100/50 = 200/100 =2 & thus this sequence is also Progression. This type of progression is called Geometric Progression

A sequence a1, a2, a3, …, an, … is called geometric progression, if each term is non-zero and a_{k+1 }/ a_{k} = r, for k ≥ 1 and r is constant.

Also GP can be written as: a, ar, ar^{2}, ar^{3},…., where a is called the first term and r is called common ratio of the G.P.

**Numerical**: Tell if the sequence is in GP or not? 1,3,9,27,51

**Solution**: A sequence a1, a2, a3, …, an, … is called geometric progression, if each term is non-zero and a_{k+1 }/ a_{k} = r, for k ≥ 1 and r is constant

3/1 = 9/3 = 27/9 ≠ 51/27

Since all the ratios are not equal, it is not a GP.

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