geometric progession help

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  1. dongonaeatu's Avatar
    1 12-04-2012  20:51
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    geometric progession help
    first two terms of geometric progression are 10 and 4
    i. find the sum of the first 15 terms
    ii. find the sum to infinity in exact form

    so sn=a(r^n-1)/r-1 a=10 n=15 and r=0.4

    s15=10(0.4^14)/0.4-1= -4.473924267*10^-2 is this right?
  2. f1mad's Avatar
    2 12-04-2012  20:54
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    Re: geometric progession help
    No it's not.

    You seem to be missing a -1 in the numerator and it's to the power 15.
  3. TenOfThem's Avatar
    3 12-04-2012  20:55
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    Re: geometric progession help
    it is r^n-1
  4. ztibor's Avatar
    4 12-04-2012  20:57
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    Re: geometric progession help
    (Original post by dongonaeatu)
    first two terms of geometric progression are 10 and 4
    i. find the sum of the first 15 terms
    ii. find the sum to infinity in exact form

    so sn=a(r^n-1)/r-1 a=10 n=15 and r=0.4

    s15=10(0.4^14)/0.4-1= -4.473924267*10^-2 is this right?
    No.

    \displaystyle s_n=a\frac{r^n-1}{r-1} \rightarrow s_{15}=10\cdot \frac{0.4^{15}-1}{0.4-1}
    and the sum of infinity for |r|<1

    \displaystyle s=a\frac{1}{1-r}
    Last edited by ztibor; 12-04-2012 at 21:01.
  5. raheem94's Avatar
    5 12-04-2012  20:58
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    Re: geometric progession help
    (Original post by dongonaeatu)
    first two terms of geometric progression are 10 and 4
    i. find the sum of the first 15 terms
    ii. find the sum to infinity in exact form

    so sn=a(r^n-1)/r-1 a=10 n=15 and r=0.4

    s15=10(0.4^14)/0.4-1= -4.473924267*10^-2 is this right?
    The formula for sum is, \displaystyle S_n =\frac{a(r^{n}-1)}{r-1}

    So inputting the values gives,
    \displaystyle S_{15}=\frac{10(0.4^{15}-1)}{0.4-1}
  6. dongonaeatu's Avatar
    6 12-04-2012  21:00
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    Re: geometric progession help
    (Original post by ztibor)
    No.

    \displaystyle s_n=a\frac{r^n-1}{r-1}
    and the sum of infinity for |r|<1

    \displaystyle s=a\frac{1}{1-r}
    i got 1.666638771 but i guess thats wrong too as its the sum of the first 15 terms and the first term is 10
  7. dongonaeatu's Avatar
    7 12-04-2012  21:01
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    Re: geometric progession help
    (Original post by raheem94)
    The formula for sum is, \displaystyle S_n =\frac{a(r^{n}-1)}{r-1}

    So inputting the values gives,
    \displaystyle S_{15}=\frac{10(0.4^{15}-1)}{0.4-1}
    raheem you tank

    is the answer 16.66664877
  8. dongonaeatu's Avatar
    8 12-04-2012  21:02
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    Re: geometric progession help
    (Original post by ztibor)
    No.

    \displaystyle s_n=a\frac{r^n-1}{r-1} \rightarrow s_{15}=10\cdot \frac{0.4^{15}-1}{0.4-1}
    and the sum of infinity for |r|<1

    \displaystyle s=a\frac{1}{1-r}
    thats wrong the a should be above the division line
  9. raheem94's Avatar
    9 12-04-2012  21:02
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    Re: geometric progession help
    (Original post by dongonaeatu)
    raheem you tank

    is the answer 16.66664877
    Yes
  10. raheem94's Avatar
    10 12-04-2012  21:03
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    Re: geometric progession help
    (Original post by dongonaeatu)
    thats wrong the a should be above the division line
    It doesn't matters, ztibor is correct.
  11. dongonaeatu's Avatar
    11 12-04-2012  21:15
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    Re: geometric progession help
    (Original post by raheem94)
    It doesn't matters, ztibor is correct.
    ah okay. What is the formula for the sum to infinity
  12. TenOfThem's Avatar
    12 12-04-2012  21:18
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    Re: geometric progession help
    (Original post by dongonaeatu)
    ah okay. What is the formula for the sum to infinity
    ztibor has given you that
  13. dongonaeatu's Avatar
    13 12-04-2012  21:23
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    Re: geometric progession help
    (Original post by ztibor)
    No.

    \displaystyle s_n=a\frac{r^n-1}{r-1} \rightarrow s_{15}=10\cdot \frac{0.4^{15}-1}{0.4-1}
    and the sum of infinity for |r|<1

    \displaystyle s=a\frac{1}{1-r}
    it says find the sum to infinity in exact form so.

    sum to infinity= 10/1-0.4= 16.6?
  14. dongonaeatu's Avatar
    14 12-04-2012  21:24
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    Re: geometric progession help
    (Original post by TenOfThem)
    ztibor has given you that
    is the sum to infinity 16.6
  15. TenOfThem's Avatar
    15 12-04-2012  21:26
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    Re: geometric progession help
    10/0.6 = 100/6 = 50/3

    you seem to have rounded so that would not be exact form
  16. dongonaeatu's Avatar
    16 12-04-2012  21:26
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    Re: geometric progession help
    (Original post by raheem94)
    It doesn't matters, ztibor is correct.
    is the sum to infinity 16.6
  17. raheem94's Avatar
    17 12-04-2012  21:26
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    Re: geometric progession help
    (Original post by dongonaeatu)
    is the sum to infinity 16.6
    Yes, it is 16.7(to 3s.f.).
  18. dongonaeatu's Avatar
    18 12-04-2012  21:27
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    Re: geometric progession help
    (Original post by TenOfThem)
    10/0.6 = 100/6 = 50/3

    you seem to have rounded so that would not be exact form
    yeah because it had lots of 6's in it lol. can i just leave it as 50/3 then?
  19. raheem94's Avatar
    19 12-04-2012  21:29
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    Re: geometric progession help
    (Original post by dongonaeatu)
    yeah because it had lots of 6's in it lol. can i just leave it as 50/3 then?
    The question asks for exact answer hence you MUST write it as \displaystyle \frac{50}3 \ or \ 16\frac23
  20. dongonaeatu's Avatar
    20 12-04-2012  21:49
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    Re: geometric progession help
    (Original post by raheem94)
    The question asks for exact answer hence you MUST write it as \displaystyle \frac{50}3 \ or \ 16\frac23
    hey man, solve 3*5^x=150 giving it to 4dp

    is it; log3*5^x=log150

    5^x=log150/log3

    5^x=4.560876795 then i dont know how to get the x on its own
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