Question

Find the first two terms of the sequence for which S_n is given below: `S_n=n^2(n+1)`

Answer 1

To find the first term, substitute n = 1 in `S_n=n^2(n+1)`

`=>S_1=1^2(1+1)=1(2)=2`

Now S₁ is the sum of the first term itself, which is also the first term. So, the first term = 2

To find the second term, substitute n = 2 in `S_n=n^2(n+1)`

`=>S_2=2^2(2+1)=4(3)=12`

Now S₂ is the sum of the first two terms.

the first term + the second term = 12

2 + the second term = 12

the second term = 12 - 2

the second term = 10

So, the first term = 2 and the second term = 10.