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arindameducationusc
 one year ago
Some Basic AP/GP information for beginners
arindameducationusc
 one year ago
Some Basic AP/GP information for beginners

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arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.14\(\Huge\color{red}{Arithmetic~Progression} \) It is a sequence in which difference of any term to its precious term is constant throughout the series. The constant difference is called common difference denoted by d. Example, 2,4,6,8,10,....... 1st term=a common difference=d last term=L AP=> a, a+d, a+2d, a+3d.....,L nth term from beginning \[T _{n}=a+(n1)d\] L=a+(n1)d Sum of AP \[S _{n}=\frac{ n }{ 2 }[2a+(n1)d]\] \(\Huge\color{Blue}{Geometric~Progression} \) It is a sequence in which the ratio of a term to its previous term is constant throughout the series. This constant ratio is called "common ratio of G.P" and is denoted by 'r' Example 2,4,8,16,32,64......... here(r)=2 1st term=a Common ratio=r nth term of GP from beginning, \[T_{n}=ar ^{n1}\] now pth term from end (L) \[T _{p}=\frac{ L }{ r ^{p1} }\] or, \[ar ^{np}\] Now sum nterms of a GP \[S _{n}=\frac{ a(r ^{n} 1)}{ r1 } , \left r \right>1\] \[S _{n}=\frac{ a(1r ^{n}) }{ 1r }\] For an infinite GP \[\left r \right <1\] i.e, 1<r<1 GP=> a+ar+ar^2+ar^3+...... infinity \[S _{\infty}=\frac{ a }{ 1r}\]

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.14I hope this tutorial helps you, for questions you are free to message me or post below.

rvc
 one year ago
Best ResponseYou've already chosen the best response.0good job:) keep up the good work :)

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.14Thank you @rvc

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.14If you want more basic info on Sequence and Series here is an awesome link by @ksanka http://openstudy.com/study#/updates/552d6fb1e4b07e661d0f5b62 See ya.! Happy learning!

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1nice :) would be great if you addd *how to find common difference and common ratio* :=)

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.14Thank you.... @rhr12 and @Nnesha ya, will post about that @Nnesha. Thanks for the tip

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.14\(\small\color{red}{As~suggested~ by~ NNesha} \) AP common difference we need to find common difference(d) d is given by \[d=T _{n}T _{n1}\] suppose a sequence 3,6,9,12,15.... d=63=129=1512=3 (all give the same) GP common ratio given by \[r=\frac{ T _{n} }{ T _{n1} }\] example suppose let a sequence be 3,9,27,81.... r=9/3=27/9=81/27
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