Find an explicit formula for the geometric sequence -40,-20,-10-.. Note: the first term should be c(1). c(n)= ?

Question

Find an explicit formula for the geometric sequence -40,-20,-10……
Note: the first term should be c(1).

c(n)= ?

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Maris 1 week 2021-07-22T17:04:28+00:00 1 Answers 2 views 0

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    2021-07-22T17:06:15+00:00

    Answer:

    The explicit formula for the geometric sequence is c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}.

    Step-by-step explanation:

    By definition of geometric sequence, we should use the following expression:

    c(n) = c_{1}\cdot r^{n-1}, n \ge 1 (1)

    Where:

    c_{1} – First term.

    r – Geometric rate.

    n – Position of the element within the series.

    If we know that c_{1} = -40 and r = \frac{1}{2}, then the explicit formula for the geometric sequence is:

    c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}

    The explicit formula for the geometric sequence is c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}.

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