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arindameducationusc

  • one year ago

Some Basic AP/GP information for beginners

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  1. arindameducationusc
    • one year ago
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    \(\Huge\color{red}{Arithmetic~Progression} \) 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 \[S _{\infty}=\frac{ a }{ 1-r}\]

  2. arindameducationusc
    • one year ago
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    I hope this tutorial helps you, for questions you are free to message me or post below.

  3. rvc
    • one year ago
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    good job:) keep up the good work :)

  4. arindameducationusc
    • one year ago
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    Thank you @rvc

  5. arindameducationusc
    • one year ago
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    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!

  6. Nnesha
    • one year ago
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    nice :) would be great if you addd *how to find common difference and common ratio* :=)

  7. rhr12
    • one year ago
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    Great job. Thank you.

  8. arindameducationusc
    • one year ago
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    Thank you.... @rhr12 and @Nnesha ya, will post about that @Nnesha. Thanks for the tip

  9. arindameducationusc
    • one year ago
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    \(\small\color{red}{As~suggested~ by~ NNesha} \) 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

  10. Nnesha
    • one year ago
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    :=)

  11. madhu.mukherjee.946
    • one year ago
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    nice

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