Deepak Bora
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3, 3 + √2, 3 + 2√2, 3 + 3√2. If this question forms an A.P then find c.d and the next four terms of the series.

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The following question is of NCERT Book class 10th Chapter no.5, Q. 5(v). In this question you have to find that is the question  an A.P or not. If it is an A.P  then find the common difference  and write 3 more values of the series.

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  1.  3, 3+√2, 3+2√2, 3+3√2

    a2 – a1 = 3+√2-3 = √2

    a3 – a2 = (3+2√2)-(3+√2) = √2

    a4 – a3 = (3+3√2) – (3+2√2) = √2

    In the series the common difference is same every time.

    So, d = √2 and this series forms a A.P.

    Now the next three terms of the series will be:-

    a5 = (3+√2) +√2 = 3+4√2

    a6 = (3+4√2)+√2 = 3+5√2

    a7 = (3+5√2)+√2 = 3+6√2

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  2. Solution:

    3, 3+√2, 3+2√2, 3+3√2

    The difference between the above valuse are:-

    a2 – a1 = 3+√2-3 = √2

    a3 – a2 = (3+2√2)-(3+√2) = √2

    a4 – a3 = (3+3√2) – (3+2√2) = √2

    In the series the common difference is same every time.

    So, d = √2 and this series forms a A.P.

    Now the next three terms in the series will be:-

    a5 = (3+√2) +√2 = 3+4√2

    a6 = (3+4√2)+√2 = 3+5√2

    a7 = (3+5√2)+√2 = 3+6√2

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