How do you find the first three iterate of the function f(x)=3x+5 for the given initial value x_0=-4?

Jan 22, 2017

$\left({x}_{1} , {x}_{2} , {x}_{3}\right) = \left(- 7 , - 16 , - 43\right)$

Explanation:

|'ve never actually seen it expressed in this form but what I assume is meant by the iterations is:
$\textcolor{w h i t e}{\text{XXX}} {x}_{1} = f \left({x}_{0}\right)$
$\textcolor{w h i t e}{\text{XXX}} {x}_{2} = f \left({x}_{1}\right)$
$\textcolor{w h i t e}{\text{XXX}} {x}_{3} = f \left({x}_{2}\right)$
...and so on

If this is the case, then given $f \left(x\right) = 3 x + 5$ and ${x}_{0} = - 4$,
we have:
$\textcolor{w h i t e}{\text{XXX}} {x}_{1} = f \left(- 4\right) = 3 \cdot \left(- 4\right) + 5 = - 12 + 5 = - 7$
$\textcolor{w h i t e}{\text{XXX}} {x}_{2} = f \left(- 7\right) = 3 \cdot \left(- 7\right) + 5 = - 21 + 5 = - 16$
$\textcolor{w h i t e}{\text{XXX}} {x}_{3} = f \left(- 16\right) = 3 \cdot \left(- 16\right) + 5 = - 48 + 5 = - 43$