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    If the first term of a geometric progression is 2 and the common ratio is 3, then what will be the fifth term of the geometric progression?
    Question

    If the first term of a geometric progression is 2 and the common ratio is 3, then what will be the fifth term of the geometric progression?

    A.

    243

    B.

    324

    C.

    81

    D.

    162

    Correct option is D

    Given:

    First term (a) = 2
    Common ratio (r) = 3

    Formula Used:
    The n-th term of a geometric progression is given by the formula:

    Tn=a×rn1T_n = a \times r^{n-1}​​

    Where:

    TnT_n is the n-th term,

    a is the first term,

    r is the common ratio, and

    n is the term number.

    Solution:
    For the fifth term (n = 5):

    T5=2×351=2×34T_5 = 2 \times 3^{5-1} = 2 \times 3^4​​

    T5=2×81=162T_5 = 2 \times 81 = 162​​

    The fifth term of the geometric progression is 162.

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