linear/series formula using ti-84+?

So, basically want a recursive sequence. So for your example, you would have:

{ s[0] = 60

{ s[n] = 0.05*s[n−1] + s[n−1], for integer n ≥ 1

There are two ways to solve this: (1) Write s[n] in explicit form, or (2) Use your calculator.

(1) Explicit forms

Note that s[n] can be written as s[n] = 1.05s[n−1]. In other words, for each increase of 1 in n, there is an increase of 1.05 times in s[n]. Since we know that the first term s[0] = 60, that means 60 will increase by 1.05 times for every 1 increase in n.

We can thus write s[n] explicitly: s[n] = 60*1.05^n, for integer n ≥ 0.

Now you can use this as you would any power series; if you wanted to know the value of s[10], you would just compute s[10] = 60*1.05^(10) ≈ 97.734

(2) Using the calculator

You can use recursive sequences by changing your graphing mode to Seq mode via the [Mode] menu.

Press [Y=]. For your example, this is what you should fill in:

nMin = 0

u(n) = 0.05u(n−1)+u(n−1)

u(nMin) = 60

You can type in n by pressing the [X,T,θ,n] button. You can type in u by pressing [2nd][7].

Once you have that, exit back to the home screen. If you want to compute u(10), then you would just type in u(10), and you should get the same answer as above.

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