Basic Math Question - Sequences and Series.

Write down the first 5 terms of the following sequence.

x(n) = 3x(n-1) - 2x(n-2), x(1) = 5, x(2) = 4


*Please Note: (n) (n-1) (n-2) (1) and (2) are all little letters/numbers.

Just need this question answered by someone who's done this sort of stuff before. I can tell it's quite simple, the right process is needed though.

Please show working! <3 Thankyou so much.

It may be a little easier to type subscripts using the _ symbol, so x_2 is x with a little 2 next to it :)

Anyway, we have:
x_n = 3x_(n-1) - 2x_(n-2)
x_1 = 5
x_2 = 4

Since we know the first two terms, next we will be looking for the third term, or x_3. We know from the relationship given that, after plugging in 3 for n:
x_3 = 3x_(3-1) - 2x_(3-2)
or
x_3 = 3x_2 - 2x_1

Since we know x_1 = 5 and x_2 = 4, we just plug in those values:
x_3 = 3(4) - 2(5)
x_3 = 12 - 10
x_3 = 2

Now that we know x_3, we have enough information to look for x_4. We proceed as before:
x_4 = 3x_(4-1) - 2x_(4-2)
x_4 = 3x_3 - 2x_2

and since we know x_3 = 3 and x_2 = 4,
x_4 = 3(2) - 2(4)
x_4 = 6 - 8
x_4 = -2

Almost finished! We just need to find x_5. I'm sure you see the pattern now:
x_5 = 3x_4 - 2x_3

and since x_4 = -2 and x_3 = 2,
x_5 = 3(-2) - 2(2)
x_5 = -6 - 4
x_5 = -10

So, the first five terms of your sequence are:
5, 4, 2, -2, -10

It might be worthwhile to note that the difference between each term doubles every time. Using this information, plus the information that we started with, you can say that:
x_n = 6 - (0.5 * 2^n)

which is the closed form of the relationship that defines the sequence. This way, you don't have to count up each time you want the n'th term in the sequence. This comes in handy when you want to know, say, the thousandth term!