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20 October, 09:33

the first term of a geometeic series is 1, the common ratio is 2, and the sum of the series is 63. How many terms are there in this geonetric series?

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  1. 20 October, 09:53
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    6 terms

    Step-by-step explanation:

    To find the number of terms we will use the formula:

    Sn = a (1-r^n) / 1-r

    where a is the first term = 1

    r is the common ratio = 2

    Sn is the sum of series = 63

    n is the number of terms = ?

    Now substitute the values in the formula:

    Sn = a (1-r^n) / 1-r

    63 = 1 (1-2^n) / 1-2

    63=1 (1-2^n) / -1

    63*-1 = 1 (1-2^n)

    -63 = 1-2^n

    Now combine the constants:

    -63-1 = - 2^n

    -64 = - 2^n

    64 = 2^n

    2^6 = 2^n

    When the base are same powers are equal to each other.

    6=n

    Thus there are 6 terms ...
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