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kmeds16

  • 3 years ago

Given a geometric sequence whose sum of the first 10 terms is 4 and whose sum from the 11th to the 30th term is 48, find the sum from the 31st to the 60th term.

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  1. cwrw238
    • 3 years ago
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    Sum of 10 = a * (r^4 - 1) -------- = 4 r- 1

  2. kmeds16
    • 3 years ago
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    @cwrw238 why is it r^4? I thought it's r^10.

  3. hitten101
    • 3 years ago
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    n is 10 not 4

  4. amistre64
    • 3 years ago
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    hmm, given is: \[S_n=\frac{1-r^n}{1-r}\] \[S_{10}=4=\frac{1-r^{10}}{1-r}\] \[S_{30-10}=48=\frac{1-r^{20}}{1-r}\]

  5. kmeds16
    • 3 years ago
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    @hitten101 yes yes :)

  6. shubhamsrg
    • 3 years ago
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    you have been given the sum upto first 10 terms =4 you have also been given the sum upto first 30 terms = 4 + 48 =52 and you have 2 eqns with 2 variables ->solve for a and r now calculate sum for first 60 terms from that subtract sum of first 30 terms.. this should help..

  7. hitten101
    • 3 years ago
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    |dw:1351514867224:dw|

  8. kmeds16
    • 3 years ago
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    a(r^10 - 1) / r - 1 = 4 a(r^30 - 1) / r - 1 = 52 ? @shubhamsrg like this?

  9. hitten101
    • 3 years ago
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    solve for a and r.. then find the sum of 60 terms subtract sum of 30 terms from sum of 60 terms

  10. shubhamsrg
    • 3 years ago
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    @kmeds16 yep @hitten101 mistake in your formulla in the denominator..

  11. kmeds16
    • 3 years ago
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    I got, r^10 = 3. this is confusing :/ 10th root of 3?!

  12. cwrw238
    • 3 years ago
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    my mistake r^10 not r^4

  13. shubhamsrg
    • 3 years ago
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    how'd you get that? o.O

  14. shubhamsrg
    • 3 years ago
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    ahh k..got it

  15. hitten101
    • 3 years ago
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    @kmeds16 @shubhamsrg yes no exponent in the denominator.. you are right

  16. kmeds16
    • 3 years ago
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    second equation divided by first equation. hehehehehe

  17. shubhamsrg
    • 3 years ago
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    your main aim is not to find r,, your main aim is to find sum.. leave it as r^10 = 3

  18. kmeds16
    • 3 years ago
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    find the sum of S60 and subtract 52, right?

  19. shubhamsrg
    • 3 years ago
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    seems likely..

  20. shubhamsrg
    • 3 years ago
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    do this,,this might simplify.. substitue r^10 =3 whereever you can leave r-1 as it is.. you can see a/(r-1) = 4/(r^10 -1) in calculation for sum of 60 terms ,make use of this eqn,, no need to find a.. :)

  21. shubhamsrg
    • 3 years ago
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    r^60 we all can find.. hmm.. hope that helped..

  22. kmeds16
    • 3 years ago
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    solving...hehehe ahm, thanks for the idea..

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