Geometric Progression Explicit Formula

Algebra Level 1

Which of the following is the explicit formula for the geometric progression

$5, 10, 20, 40, \dots?$

2 \cdot 5^{n-1}

5 \cdot 2^{n-1}

5 \cdot 2^{n+1}

5 \cdot 5^{n}

1 solution

Jordan Cahn
Oct 23, 2018

A geometric progression has the general formuala (a\cdot r^n), where $a$ is the starting value and $r$ is the ratio between successive terms. Here, we start at $a=5$ and successive terms have a ration of $r=2$ . We use an exponent of $n-1$ instead of $n$ since we wish to begin counting from the first term, instead of the zeroth. $\boxed{5\cdot 2^{n-1}}$

Geometric Progression Explicit Formula

1 solution

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