arindameducationusc
  • arindameducationusc
Some Basic AP/GP information for beginners
Pre-Algebra
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
arindameducationusc
  • arindameducationusc
\(\Huge\color{red}{Arithmetic~Progression} \) 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 a+ar+ar^2+ar^3+...... infinity \[S _{\infty}=\frac{ a }{ 1-r}\]
arindameducationusc
  • arindameducationusc
I hope this tutorial helps you, for questions you are free to message me or post below.
rvc
  • rvc
good job:) keep up the good work :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

arindameducationusc
  • arindameducationusc
Thank you @rvc
arindameducationusc
  • arindameducationusc
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!
Nnesha
  • Nnesha
nice :) would be great if you addd *how to find common difference and common ratio* :=)
rhr12
  • rhr12
Great job. Thank you.
arindameducationusc
  • arindameducationusc
Thank you.... @rhr12 and @Nnesha ya, will post about that @Nnesha. Thanks for the tip
arindameducationusc
  • arindameducationusc
\(\small\color{red}{As~suggested~ by~ NNesha} \) 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
Nnesha
  • Nnesha
:=)
madhu.mukherjee.946
  • madhu.mukherjee.946
nice

Looking for something else?

Not the answer you are looking for? Search for more explanations.