# A sequence is defined recursively using the equation f (n+1)=f (n)-8. If f (1)=100, what is f (6)?

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Steve M Share
Jul 9, 2017

$f \left(6\right) = 60$

#### Explanation:

We have:

$f \left(1\right) = 100$
$f \left(n + 1\right) = f \left(n\right) - 8$

Put $n = 1$ and we get:

$f \left(2\right) = f \left(1\right) - 8$
$\text{ } = 100 - 8$
$\text{ } = 92$

Put $n = 2$ and we get:

$f \left(3\right) = f \left(2\right) - 8$
$\text{ } = 92 - 8$
$\text{ } = 84$

Put $n = 3$ and we get:

$f \left(4\right) = f \left(3\right) - 8$
$\text{ } = 84 - 8$
$\text{ } = 76$

Put $n = 4$ and we get:

$f \left(5\right) = f \left(4\right) - 8$
$\text{ } = 76 - 8$
$\text{ } = 68$

Put $n = 5$ and we get:

$f \left(6\right) = f \left(5\right) - 8$
$\text{ } = 68 - 8$
$\text{ } = 60$

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