Question

Solve this qwestiin with explains Plz ☺️​

Answer 1

Answer:

2n - 1

Step-by-step explanation:

Given : ${\sf{\ \ S_n = n^2 + 4}}$

If we subtract the sum of (n - 1) terms, we can get the ${\sf{n^{th}}}$ term.

From above equation, we can get the following equation :

→ ${\sf{S_{n - 1} = (n - 1)^2 + 4}}$

On further solving, we get

☯ { Identity : (a - b)² = a² - 2ab + b²

Here, a = n, b = 1 }

→ ${\sf{S_{n - 1}}}$ = n² - 2n + 1 + 4

→ ${\sf{S_{n - 1}}}$ = n² - 2n + 5

Now, to find the ${\sf{n^{th}}}$ term, we have to subtract ${\sf{S_n}}$ and ${\sf{S_{n - 1}.}}$

→ ${\sf{t_n = S_n - S_{n - 1}}}$

Putting known values, we get

→ ${\sf{t_n = n^2 + 4 - (n^2 - 2n + 5)}}$

→ ${\sf{t_n = n^2 + 4 - n^2 + 2n - 5}}$

→ ${\sf{t_n = 2n - 1}}$

Hence, the ${\sf{n^{th}}}$ term is 2n - 1.

Answer 2

Given : Sn = n² + 4

If we subtract the sum of (n - 1) terms, we can get the ${\tt{n^{th}}}$ term.

From above equation, we can get the following equation :

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

By Simplifying it , we get

__________________ Identity used: (a - b)² = a² - 2ab + b²

Here,

•a = n

• b = 1

${\tt{S_{n - 1}}}$ = n² - 2n + 1 + 4

${\tt{S_{n - 1}}}$ = n² - 2n + 5

Now, we have to find the {\sf{n^{th}}}[/tex] term, now we subtract ${\tt{S_n}}$ and ${\tt{S_{n - 1}.}}$

${\tt{t_n = S_n - S_{n - 1}}}$

By substituting the known values, we get

${\tt{t_n = n^2 + 4 - (n^2 - 2n + 5)}}$

${\tt{t_n = n^2 + 4 - n^2 + 2n - 5}}$

${\tt{t_n = 2n - 1}}$

Hence, the ${\tt{n^{th}}}}$ term is 2n - 1