Question

Find the first two terms of the sequence sn=


n^2 (n+1)

Answer 1

Given ::- Sn = n²(n+1)

Solution ::-

We know that,

Sn = n/2[ 2a + (n-1)d ]

n² (n+1) = n/2 [ 2a + (n-1)d]

Putting n as 1 , to get value of 'a'

(1)² (1+1) = 1/2 [ 2a + (1-1)d]

1 (2) = 1/2 [ 2a + 0 ]

2. = a

Taking n as 2 to get value of d

(2)²(2+1) = 2/2 [ 2a + (2-1)d]

4 (3). = 1 [ 2(2) + d ]

12. = 4 + d

12 - 4 = d

8 = d

So, d is 8

2nd term = a + d

= 2 + 8

= 10

There fore the first term of AP is 2 and the second term of AP is 10

HOPE IT HELPS YOU!!

Answer 2

keep the values of n as 1 and 2 resp. and find s1 and s2

as s1 =a hence s2=a+a2

so a2 = s2-s1

and we get the answers which are a=2 and a2=10