Geometric series formulas

A geometric series is a sequence of numbers for which the ratio of each two consecutive terms is a constant number.

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First term

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n-th term

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Common ratio

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Number of terms

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Sum of first n terms

n-th term

$a_n=a_1\cdot q^{n-1}$

Sum of first n terms

$S_n = a_1\frac{q^n-1}{q-1}$

Sum of first n terms

$S_n = \dfrac{a_nq-a_1}{q-1}$

Sum of infinite geometric series

$S=\dfrac{a_1}{1-q}, \text{for} |q| < 1$

Common raito

$q=\dfrac{a_n}{a_1}$