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- by Ashok Shah 4 months ago

Introduction to Sequence and Series

Arithmetic series__Some of the step in the note below are skipped so check the notes above as reference for ease__

→The sequence whose common ratio between the two successive terms are same is called geometric sequence.

For example:3, 9, 27, 81……..

General term of Geometric Progression is given by;

→** ****t**_{n}**=ar**^{n-1}

where,

** t**_{n}**= n**^{th}** term of sequence a = first term of sequence n = nth term of sequence r = common ratio of sequence**

Geometric Mean: The term/s in between the first and last term in the arithmetic progression is/are called geometric means.

Example; i) 2, 4, 8 ii) 4, -8, 16, -32, 64

Here, the highlighted terms are the geometric means.

__Formulas related to Geometric Means:__

→The single geometric mean between two terms a & b is calculated by;

→If there are n terms between ‘a’ and ‘b’ then the common ratio is given by;

*Here, n does represent number of terms in the sequence but number of means between first and last term.*

→n^{th} mean=ar^{n}

__Sum of GP__

→ [when 1st term and number of terms are given & r >1]

→ [when 1st term and number of terms are given & r <1]

→ [when 1st and last terms are given & r >1]

→ [when 1st and last terms are given & r <1]

^{}

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