​Given the following sequence:

5, 10, 15, 20, ...

Is there a geometric pattern?

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Sometimes...there is NO geometric pattern.​

​Finding specific terms from an geometric sequence:

formula: a_n = a₁ * r^n-1

a₁: first term in the sequence

r: common ratio

n: the term location you want to calculate

Example:

Given: 5, 20, 80, ...

a₁ = 5 and r = ​4

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Formula: ​a_n=5*4^(n-1)

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Replace the n for the desired term needing to calculate.​

​Scenarios:

The following table shows a car's value for 3 years after it is purchased.

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Writing the equation:

a₁ = 10000 and r = 4/5​

an = 10000 * 4/5^{n - 1}

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​Predict the value of the car after 10 years: $1,342.18​