NCERT Solutions Class 11th Maths Chapter – 9 Sequences and Series Exercise 9.4
| Textbook | NCERT |
| class | Class – 11th |
| Subject | Mathematics |
| Chapter | Chapter – 9 |
| Chapter Name | Sequences and Series |
| grade | Class 11th Maths solution |
| Medium | English |
| Source | last doubt |
NCERT Solutions Class 11th Maths Chapter – 9 Sequences and Series Exercise 9.4
?Chapter – 9?
✍Sequences and Series✍
?Exercise 9.4?
1. 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
?♂️solution – Given series is 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
It’s seen that,
nth term, an = n ( n + 1)
Then, the sum of n terms of the series can be expressed as
2. 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …
?♂️solution – Given series is 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …
It’s seen that,
nth term, an = n ( n + 1) ( n + 2)
= (n2 + n) (n + 2)
= n3 + 3n2 + 2n
Then, the sum of n terms of the series can be expressed as
3. 3 × 12 + 5 × 22 + 7 × 32 + …
?♂️solution – Given series is 3 ×12 + 5 × 22 + 7 × 32 + …
It’s seen that,
nth term, an = ( 2n + 1) n2 = 2n3 + n2
Then, the sum of n terms of the series can be expressed as
4. Find the sum to n terms of the series
?♂️solution –
5. Find the sum to n terms of the series 52 + 62 + 72 + … + 202
?♂️solution – Given series is 52 + 62 + 72 + … + 202
It’s seen that,
nth term, an = ( n + 4)2 = n2 + 8n + 16
Then, the sum of n terms of the series can be expressed as
6. Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…
?♂️solution – Given series is 3 × 8 + 6 × 11 + 9 × 14 + …
It’s found out that,
an = (nth term of 3, 6, 9 …) × (nth term of 8, 11, 14, …)
= (3n) (3n + 5)
= 9n2 + 15n
Then, the sum of n terms of the series can be expressed as
7. Find the sum to n terms of the series 12 + (12 + 22) + (12 + 22 + 32) + …
?♂️solution – Given series is 12 + (12 + 22) + (12 + 22 + 32 ) + …
Finding the nth term, we have
an = (12 + 22 + 32 +…….+ n2)
Now, the sum of n terms of the series can be expressed as
8. Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).
?♂️solution – Given,
an = n (n + 1) (n + 4) = n(n2 + 5n + 4) = n3 + 5n2 + 4n
Now, the sum of n terms of the series can be expressed as
9. Find the sum to n terms of the series whose nth terms is given by n2 + 2n
?♂️solution – Given,
nth term of the series as:
an = n2 + 2n
Then, the sum of n terms of the series can be expressed as
10. Find the sum to n terms of the series whose nth terms is given by (2n – 1)2
?♂️solution – Given,
nth term of the series as –
an = (2n – 1)2 = 4n2 – 4n + 1
Then, the sum of n terms of the series can be expressed as
