Question

-If the sum of first 8 terms of an AP is 64 and the sum of first 12 terms is
144, find the sum of n terms of an AP. ​

Answer 1

Answer:

n^2

Step-by-step explanation:

In AP ,suppose first term is a and common difference term is d

So, equation (1)

8/2 [ 2a + (8 - 1)d ] =64

2a + 7d =8 * 2

2a + 7d = 16

equation (2)

12/2 [ 2a +(12 - 1)d] =144

2a + 11d=12 * 2

2a + 11d=24

Now subtract equation (1) from equation (2)

2a+11d=24

2a+7d=16

- - -

__________

4d= 8

d=2

Then put d=2 in equation (2) to get a

2a+11d = 24

2a+ 11*2= 24

2a + 22= 24

2a=24 - 22

2a= 2

a = 1

Now, Sn = n/2(2a + (n-1)d)

= n/2( 2 +(n-1)2). (take 2 common)

= n(1 +n - 1)

= n*n

= n^2