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Math Help - Progression

  1. #1
    Member princess_anna57's Avatar
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    Progression

    The seventh term of a geometric progression is 0.775 and the ninth term is 0.995.
    (a) Find the common ratio (to 3 decimal places).
    (b) List the first three terms of the geometric progression (to 6 decimal places).
    (c) Find the sum of the first ten terms (to 3 decimal places).
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    The seventh term of a geometric progression is 0.775 and the ninth term is 0.995.
    (a) Find the common ratio (to 3 decimal places).
    (b) List the first three terms of the geometric progression (to 6 decimal places).
    (c) Find the sum of the first ten terms (to 3 decimal places).
    recall that the terms of a geometric progression are given by

    a_n = ar^{n - 1} for n = 1,~2,~3, \dots

    where a_n is the nth term, a is the first term, r = \frac {a_2}{a_1} = \frac {a_3}{a_2} = \cdots is the common ratio.

    thus, we have the 7th term is ar^6 = 0.775 and the 9th term is ar^8 = 0.995

    so, \frac {ar^8}{ar^6} = \frac {0.995}{0.775}

    you can use that to find r, once you have r you can find a. once you have a and r, you can answer all the questions

    good luck


    EDIT: also, recall that the sum S_n of the first n terms is given by S_n = a \cdot \frac {1 - r^n}{1 - r}
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