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`T_(n)=2^(n)` <br> `rArr" "T_(n-1)=2n^(n-1)` <br> `therefore" "T_(n)/(T_(n-1))=(2^(n))/2^(n-1)=2` <br> which does not depend on n. <br> Therefore, given progression is G.P. Hence Proved. Its common ratio is 2.**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**

**The `n^(th)` term of the sequence is `3n-2` . Is the sequence an AP. If so; find the 10th term .**

**If first term is 8 and last term is 20 common diffference is 2 . find the value of n when the series are in AP.**

**Which term of the sequence is the first negative term .. `20; 19(1/4);18(1/2);17(3/4).....`**

**Show that the sum of `(m+n)^(th) and (m-n)^(th)` term of an AP is equal to twice the `m^(th)` term ?**

**Show that sum `S_n` of n terms of an AP with first term a and common difference d is `S_n=n/2(2a+(n-1)d)`**

**Find the sum of 20 terms of the AP 1, 4, 7, 10,....**