11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer \[{{n}^{th}}\] term of the series\[1+\frac{4}{5}+\frac{7}{{{5}^{2}}}+\frac{10}{{{5}^{3}}}+........\]will be

    A) \[\frac{3n+1}{{{5}^{n-1}}}\]

    B) \[\frac{3n-1}{{{5}^{n}}}\]

    C) \[\frac{3n-2}{{{5}^{n-1}}}\]

    D) \[\frac{3n+2}{{{5}^{n-1}}}\]

    Correct Answer: C

    Solution :

    This series is clearly an A.G., the corresponding A.P. is \[1+4+7+10+.........\]having \[{{n}^{th}}\]term \[=3n-2\] and corresponding G.P. is  \[1+\frac{1}{5}+\frac{1}{{{5}^{2}}}+.........\] having \[{{n}^{th}}\]term \[=\frac{1}{{{5}^{n-1}}}\] Hence required \[{{n}^{th}}\]term of the series is \[\frac{3n-2}{{{5}^{n-1}}}\]. Trick: Check by putting \[n=1,\ 2\] in alternates.

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