1. ## Basic Sequence

if
tn+1=2tn+tn-1

t1=1
t2=3

What's the next 3 numbers of the sequence?

I don't understand the question - anyone help?

2. 7, 17, 41

3. yea - but i don't understand why - anyone explain?

4. t_(n + 1) = 2t_n + t_(n - 1) is equivalent to t_n = 2t_(n - 1) + t_(n - 2).

5. For example, let n = 3. t_3 = 2t_(3 - 1) + t_(3 - 2) = 2t_2 + t_1 = 2 · 3 + 1 = 7. Repeat for n = 4 and 5.

6. Oh ok - I kind of get it
But Johnny - you said :

t_(n + 1) = 2t_n + t_(n - 1) is equivalent to t_n = 2t_(n - 1) + t_(n - 2).

How did you get from the first equation to the second?
Is there an algebraic operation that i can do ?

7. t_(n + 1) = 2t_n + t_(n - 1) is read as third number is equal to 2 times second number plus first number, hence n, n - 1 and n - 2 is logically the same thing.
Also, I did this because it's easier to calculate the third number.

8. So no algebra steps whatsoever?
..
ok then
Thanks anyways

9. Hello, qwertyuiop!

If t(n+1) = 2t(n) + t(n-1) . and t(1) = 1, t(2) = 3,

what are the next 3 numbers of the sequence?

It seems that you don't understand that the equation says:

. . "A term is equal to twice the preceding term, plus the term before that."

We have: .t(1) = 1

. . . . . . . .t(2) = 3

Then: .t(3) .= .2(3) + 1 .= .7

Then: .t(4) .= .2(7) + 3 .= .17

Then: .t(5) .= .2(17) + 7 .= .41

Get it?

10. ohh i see i see
Thanks !