Petra records the score in each test she takes.

The mean of the first n scores is x.
The mean of the first (n-1) scores is (x+1).

Find the nth score in terms of n and x. Give your answer in its simplest form.

Respuesta :

Answer:

[tex]x-n+1[/tex]

Step-by-step explanation:

Given the mean of [tex]n[/tex] terms as [tex]x[/tex], and of [tex]n-1[/tex] as [tex]x+1[/tex]:

We know that  [tex]\bar X=\frac{1}{n}\sum x_i[/tex] for [tex]n[/tex] terms.

Therefore [tex]\sum x_n=n \bar X[/tex] for [tex]n[/tex] terms;

For [tex]n-1[/tex]  terms; [tex]\sum x_n_-_1=(n-1)(x+1)=nx-x+n-1[/tex]

To find the nth score, we subtract the sum of (n-1) terms from the sum of n terms:

[tex]n^t^h[/tex] term=

[tex]nx-(nx-x+n-1)\\=x-n+1[/tex]