Question

the sum of first n terms of an AP is given by(n^2+8n).find the 12th term of AP also find the nth term of the AP​

Answer 1

Step-by-step explanation:

Sn=n^2+8n

S1=a

S1=1^2+8*1

=9

a=9

S2-a=a2

S2=2^2+8*2

=20

20-9=11

a2=11

d=11-9=2

d=2

a12=a+11d

a12=9+22

a12=31

an=9+(n-1)2

9-2+2n

7+2n

Answer 2

Answer:

nth term is  $2n+7$ and 12th term is 31.

Step-by-step explanation:

Given :The sum of first n terms of an AP is given by $(n^2+8n)$

To Find : Find the 12th term of AP also find the nth term of the AP​

Solution:

We are supposed to find the 12th term of AP .

To find 12th term we need to subtract the sum of first 11 terms from sum of first 12 terms .

$S_n=(n^2+8n)$

Substitute n = 12

$S_{12}=(12^2+8(12))$

$S_{12}=240$

$S_n=(n^2+8n)$

Substitute n = 11

$S_{11}=(11^2+8(11))$

$S_{11}=209$

12th term = $S_{12}-S_{11}$

12th term = 240-209

12th term = 31

To find nth term we need to subtract the sum of first (n-1) terms from sum of first n terms.

Substitute n = n-1

$S_{n-1}=((n-1)^2+8(n-1))$

$S_{n-1}=n^2+1-2n+8n-8$

$S_{n-1}=n^2+6n-7$

nth term = $S_n-S_{n-1}$

nth term = $S_n-S_{n-1}$

nth term = $n^2+8n-(n^2+6n-7)$

nth term = $n^2+8n-n^2-6n+7$

nth term = $2n+7$

Hence nth term is  $2n+7$ and 12th term is 31.