iii.
|
Sn
|
=
|
n(n+1)(2n+1)
| ||||||
6
| |||||||||
Sol.
|
Sn
|
=
|
n(n+1)(2n+1)
| ||||||
6
| |||||||||
∴
|
S1
|
=
|
1(1+1)[2(1)+1]
|
=
|
1(2)(3)
|
=
|
6
|
=
|
1
|
6
|
6
|
6
| |||||||
∴
|
S2
|
=
|
2(2+1)[2(2)+1]
|
=
|
2(3)(5)
|
=
|
30
|
=
|
5
|
6
|
6
|
6
| |||||||
∴
|
S3
|
=
|
3(3+1)[2(3)+1]
|
=
|
3(4)(7)
|
=
|
2× 7
|
=
|
14
|
6
|
6
|
We know that,
t1 = S1 = 1
t2 = S2 – S1 = 5 – 1 = 4
t3 = S3 – S2 = 14 – 5 = 9
∴ The first three terms of the sequence are 1, 4 and 9. 