Question

Some Basic AP/GP information for beginners

Answer 1

\(\Huge\color{red}{Arithmetic~Progression} \)
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
\[T _{n}=a+(n-1)d\]

L=a+(n-1)d

Sum of AP
\[S _{n}=\frac{ n }{ 2 }[2a+(n-1)d]\]

\(\Huge\color{Blue}{Geometric~Progression} \)

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,
\[T_{n}=ar ^{n-1}\]

now pth term from end (L)

\[T _{p}=\frac{ L }{ r ^{p-1} }\]

or,

\[ar ^{n-p}\]

Now sum n-terms of a GP

\[S _{n}=\frac{ a(r ^{n} -1)}{ r-1 } , \left| r \right|>1\]

\[S _{n}=\frac{ a(1-r ^{n}) }{ 1-r }\]

For an infinite GP

\[\left| r \right| <1\]
i.e, -1<r<1

GP=> a+ar+ar^2+ar^3+...... infinity

\[S _{\infty}=\frac{ a }{ 1-r}\]

Answer 2

I hope this tutorial helps you, for questions you are free to message me or post below.

Answer 3

good job:)
keep up the good work :)

Answer 4

Thank you @rvc

Answer 5

If 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!

Answer 6

nice :)
would be great if you addd *how to find common difference and common ratio* :=)

Answer 7

Great job. Thank you.

Answer 8

Thank you.... @rhr12 and @Nnesha

ya, will post about that @Nnesha.
Thanks for the tip

Answer 9

\(\small\color{red}{As~suggested~ by~ NNesha} \)

AP common difference

we need to find common difference(d)
d is given by
\[d=T _{n}-T _{n-1}\]


suppose a sequence 3,6,9,12,15....

d=6-3=12-9=15-12=3 (all give the same)


GP common ratio given by
\[r=\frac{ T _{n} }{ T _{n-1} }\]

example
suppose let a sequence be 3,9,27,81....
r=9/3=27/9=81/27

Answer 10

:=)

Answer 11

nice