JEE Main & Advanced Mathematics Sequence & Series Question Bank Geometric Progression

  • question_answer
    Sum of infinite number of terms in G.P. is 20 and sum of their square is 100. The common ratio of G.P. is   [AIEEE 2002]

    A) 5

    B) 3/5

    C) 8/5

    D) 1/5

    Correct Answer: B

    Solution :

    \[\frac{a}{1-r}=20\]             .....(i) \[\frac{{{a}^{2}}}{1-{{r}^{2}}}=100\]            ?..(ii) From (i) and (ii), \[\frac{a}{1+r}=5\], \[\left[ \because a=20(1-r)\,\,\text{by}\,\,(i) \right]\] Þ \[\frac{20(1-r)}{1+r}=5\] \[\Rightarrow 5r=3\] Þ \[r=3/5\].


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