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11th Class Mathematics Sequence and Series Question Bank Sequence and Series (A.P., G.P. and H.P.)

  • question_answer
    There is a sequence of slumbers such that they are m GP and sum to infinite of the numbers of terms of the sequence is 6 and the sum of their squares up to infinite terms is 18. The first term of the sequence is given by:

    A)  16                               

    B)  4   

    C)  6                                

    D)  1/3

    Correct Answer: B

    Solution :

    (b): The sum of infinite number of terms in GP is given by \[{{S}_{\infty }}=\frac{a}{1-r}\] \[\Rightarrow \] \[6=\frac{a}{1-r}\]                                   ... (1) Also the sum of square of the terms of the GP is given by \[{{S}_{\infty }}=\frac{{{a}^{2}}}{1-{{r}^{2}}}\] \[\Rightarrow \]\[18=\frac{{{a}^{2}}}{1-{{r}^{2}}}\]                           ? (2) Dividing (2) by square of (1) \[\Rightarrow \]\[\frac{1}{2}=\frac{1-r}{1+r}\] Applying component do dividend do, \[\frac{1+2}{1-2}=\frac{2}{-2r}\]\[\Rightarrow \]\[r=\frac{1}{3}\] \[\Rightarrow \]\[a=4\]           


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