1. ## sequence

Here is the problem:

Define a sequence $\displaystyle c_k$ by the rules
$\displaystyle c_0$ = 2
$\displaystyle c_1$ = 3
$\displaystyle c_k = 0.8c_{k-1} - 0.7c_{k-2}$

Compute $\displaystyle c_2$ through $\displaystyle c_6$

Anyway, I really struggle with these? Where do I start? What process do I go through? Can someone please walk me through this one problem?

Thanks

2. Originally Posted by relyt
Here is the problem:

Define a sequence $\displaystyle c_k$ by the rules
$\displaystyle c_0$ = 2
$\displaystyle c_1$ = 3
$\displaystyle c_k$ = 0.8$\displaystyle c_k-1$ - 0.7 $\displaystyle c_k-2$

Compute $\displaystyle c_2$ through $\displaystyle c_6$

Those k - 1 and k-2 should be subscripts

Anyway, I really struggle with these? Where do I start? What process do I go through? Can someone please walk me through this one problem?

Thanks
just plug in the values in the $\displaystyle c_k$ formula

example, to find $\displaystyle c_2$, plug in $\displaystyle k = 2$, you get

$\displaystyle c_2 = 0.8c_1 - 0.7c_0 = 0.8(3) - 0.7(2) = 1$

now find the rest the same way

3. Originally Posted by relyt
Here is the problem:

Define a sequence $\displaystyle c_k$ by the rules
$\displaystyle c_0$ = 2
$\displaystyle c_1$ = 3
$\displaystyle c_k = 0.8c_{k-1} - 0.7c_{k-2}$

Compute $\displaystyle c_2$ through $\displaystyle c_6$

Anyway, I really struggle with these? Where do I start? What process do I go through? Can someone please walk me through this one problem?

Thanks
You start by calculating with $\displaystyle k=2$:

$\displaystyle c_2=0.8c_1-0.7c_0=0.8\times 3 - 0.7 \times 2=1$

Now you know $\displaystyle c_0,\ c_1,\ c_2$ proceed to calculate $\displaystyle c_3$, and continue from there.

CB

4. Got it...thank you. That was a lot easier than I thought