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nth term <br> `T_(n) = (1)/(("nth term of " 1,2,3,….)("nth term of " 2, 3, 4,…))` <br> `= (1)/({1 + (n - 1) * 1}{2 + (n-1) * 1})` <br> `= (1)/(n(n + 1))` <br> `= ((n + 1) - n)/(n(n+1)) = (1)/(n) - (1)/(n+1)` <br> Put n = 1, 2, 3,…., n on both sides, <br> `T_(1) = 1 - (1)/(2)` <br> `T_(2) = (1)/(2) - (1)/(3)` <br> `T_(3) = (1)/(3) - (1)/(4)` <br> `vdots " " vdots " " vdots` <br> `T_(n) = (1)/(n) - (1)/(n + 1)` <br> Adding columnwise `S_(n) = 1 - (1)/(n + 1) = (n)/(n + 1)cdot`**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,....**