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Thread: Geometric Progression- Ans to confirm only

  1. #1
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    Geometric Progression- Ans to confirm only

    Question:
    if 1+y, 1+3y, 1+4y (y cant be 0..sorry i dont know how to write it in math equation here ) are three consecutive terms of a Geometric Progression. Find
    (a) the value of y
    (b) the sum to infinity.

    the ans from book
    (a) -1/5
    (b) 8/5

    but i have calculate and get this ans
    (a) 1/5
    (b) -18/5

    thank for your advice
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  2. #2
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    Quote Originally Posted by nikk View Post
    Question:
    if 1+y, 1+3y, 1+4y (y cant be 0..sorry i dont know how to write it in math equation here ) are three consecutive terms of a Geometric Progression. Find
    (a) the value of y
    (b) the sum to infinity.

    the ans from book
    (a) -1/5
    (b) 8/5

    but i have calculate and get this ans
    (a) 1/5
    (b) -18/5

    thank for your advice
    In a geometric progression: $\displaystyle \frac{t_{n + 1}}{t_n} = r$.


    So $\displaystyle \frac{1 + 3y}{1 + y} = r$ and $\displaystyle \frac{1 + 4y}{1 + 3y} = r$.


    Therefore $\displaystyle \frac{1 + 3y}{1 + y} = \frac{1 + 4y}{1 + 3y}$

    $\displaystyle (1 + 3y)^2 = (1 + y)(1 + 4y)$

    $\displaystyle 1 + 6y + 9y^2 = 1 + 5y + 4y^2$

    $\displaystyle 5y^2 + y = 0$

    $\displaystyle y(5y + 1) = 0$

    $\displaystyle y = 0$ or $\displaystyle 5y + 1 = 0$

    $\displaystyle y = 0$ or $\displaystyle y = -\frac{1}{5}$.


    Since $\displaystyle y \neq 0$ that means $\displaystyle y = -\frac{1}{5}$.


    Now to find the sum to infinity, we need $\displaystyle a$ and $\displaystyle r$


    $\displaystyle r = \frac{1 + 3y}{1 + y}$

    $\displaystyle = \frac{1 + 3\left(-\frac{1}{5}\right)}{1 - \frac{1}{5}}$

    $\displaystyle = \frac{1 - \frac{3}{5}}{\frac{4}{5}}$

    $\displaystyle = \frac{\frac{2}{5}}{\frac{4}{5}}$

    $\displaystyle = \frac{1}{2}$.


    Are we assuming that $\displaystyle a = 1 + y$?

    If so $\displaystyle a = \frac{4}{5}$.


    Now, since $\displaystyle |r| < 1$ we can work out the sum to infinity...

    $\displaystyle S_{\infty} = \frac{a}{1 - r}$

    $\displaystyle = \frac{\frac{4}{5}}{1 - \frac{1}{2}}$

    $\displaystyle = \frac{\frac{4}{5}}{\frac{1}{2}}$

    $\displaystyle = \frac{8}{5}$.
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  3. #3
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    tq for the post ..now i can see where my calculation wrong

    can u guide me how to make this equation in latex look more bigger

    http://www.mathhelpforum.com/math-he...ze-bigger.html
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