1, 4, 8, 13, 19, 26

Find sequence formula using the quadratic way.

1/2 n^2 + 3/2 n - 1.

Step-by-step explanation:

                      1   4    8    13    19   26

Differences      3   4     5    6      7

2nd Diff:               1     1     1      1

This means that a in the formula a^2n + bn + c =   1/2    ( as 2a = 1).

Now The first difference is 3 and we plug this into the formula:

3a - b = first difference

3(1/2) + b = 3

b =  3 - 3/2  = 3/2.

So we have the formula  1/2 n^2 + 3/2 n + c

So using the first term 1 :  1/2(1)^2 + 3/2 + c = 1

c = 1  - 3/2 - 1/2 = 1 -2 = -1.

Formula is therefore 1/2n^2 + 3/2 n - 1.

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: