HELP!!! Recursion formulas!!! PLEASE!!!!!!!?

Question

i don't get it...i have the answer key though.. please help.

determine the first 5 terms of the sequence.

T1=1, Tn-1+n, n>1
^the n-1 is tiny too :D
^the 1 up there is tiny

ya so please help!

the answer is 1, 3, 6, 10, 15 ( i think the answer key is right... )

THANKS EVERYBODY!!!
i finally understand it yay!

Answer 1

ok, n=1,2,3,4,5...
What is being done here is the nth term = the prior term + the number n, with the first term being 1.
so n=1 ==> T1 =1
n=2 ==> T2 = T1(1) + 2 = 3
n=3 ==> T3 = T2(3) + 3 = 6
n=4 ==> T4 = T3(6) + 4 = 10, and
n=5 ==> T5 = T4(10) + 5 = 15.

Hope you see the pattern.

Answer 2

It might help if you use T(n) to represent the n'th term in your recursion formula.

I think you mean T(1) = 1,
T(n) = T(n-1) + n. for n > 1

From this,
T(1) = 1, by definition
T(2) = T(1) + 2 = 1+2 = 3
T(3) = T(2) + 3 = 3 + 3 = 6
T(4) = T(3) + 4 = 6+4 = 10
T(5) = T(4) + 5 = 10+5 = 15

(If you know how to use a spreadsheet like Excel, it would be a good exercise to set up the above formula to generate T(n) for large values of n).

Answer 3

I'll use a slightly different notation
T(n) = T(n-1) + n

The "n"th value of T is the previous value T(n-1) plus n.

given: T(1) = 1
The first value of T is 1

T(2), the second value of T, is T(1)+n = 1 + 2 = 3

T(3) = T(2) + 3 = [T(1)+2] + 3 = [1+2]+3

It is called recursive because, if you are looking directly for a value of T (let us say, the 20th value, T(20)), you have to go back to the first value T(1) since that is the only one that is given.

T(20) = T(19) + 20
T(20) = [T(18)+19] + 20
T(20) = T(17) + 18 + 19 + 20
etc. until
T(20) = T(1)+2+3+4+...+17+18+19+20
Given: T(1)=1
T(20) = 1+2+3+4...+17+18+19+20