Question

If sn=4n-n square then find an =?

Answer 1

Sn = 4n-n²

Sn-1 = 4(n-1)-(n-1)²

Sn-1 =4n-4 - n² -1 +2n

Sn-1 =6n -5-n²

now, an=Sn - Sn-1 = 4n-n² -(6n -5-n²)

an= 4n-n² -6n +5+n²

an= 5-2n

Answer 2

Given :

$S_n = 4n-n^2$

To Find:

$a_n$

Solution:

We know that :

$a_n=S_n-S_{n-1}$

We are given that :

$S_n = 4n-n^2$

$S_{n-1} = 4(n-1)-(n-1)^2$

$S_{n-1} =4n-4 - n^2 -1 +2n$

$S_{n-1} =6n -5-n^2$

So,

$a_n=S_n-S_{n-1}\\a_n= 4n-n^2 -(6n -5-n^2)\\a_n= 4n-n^2 -6n +5+n^2\\a_n= 5-2n$

Hence$a_n=5-2n$