Question

Find the first three terms of the sequence below. T n = n 2 − 2 n − 3

Answer 1

Step-by-step explanation:

See title. I'm trying to apply the method from this question. What I have so far is this, but I don't know how to proceed from here on:

T(n) = T(n-1) + n2

T(n-1) = T(n-2) + (n-1)2 = T(n-2) + n2 - 2n + 1

T(n-2) = T(n-3) + (n-2)2 = T(n-3) + n2 - 4n + 4

T(n-3) = T(n-4) + (n-3)2 = T(n-4) + n2 - 6n + 9

Substituting the values of T(n-1), T(n-2) and T(n-3) into T(n) gives:

T(n) = T(n-2) + 2n2 - 2n + 1

T(n) = T(n-3) + 3n2 - 6n + 5

T(n) = T(n-4) + 4n2 - 12n + 14

Now I have to find a pattern but I don't really know how to do that. What I got is:

#khushu☺️

Answer 2

Answer:

Step-by-step explanation:

Tn= (1)^2 -2(1) -3 = 1 -2 -3= -4

Tn= (2)^2 -2(2) -3 = 4 -4 -3= -3

Tn= (3)^2 -2(3) -3 = 9 -6 -3= 0