Exercise 9.4 - Chapter 9 Sequences & Series class 11 ncert solutions Maths - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question 1:

Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

Answer:

The given series is 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

n^th term, an = n ( n + 1)

Question 2:

Find the sum to n terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

Answer:

The given series is 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

n^th term, an = n ( n + 1) ( n + 2)

= (n² + n) (n + 2)

= n³ + 3n² + 2n

Question 3:

Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …

Answer:

The given series is 3 ×1² + 5 × 2² + 7 × 3² + …

n^th term, an = ( 2n + 1) n² = 2n³ + n²

Question 3:

Find the sum to n terms of each of the series in Exercises 1 to 7.

3 × 1² + 5 × 2² + 7 × 3² + …

Answer:

The given series is 3 ×1² + 5 × 2² + 7 × 3² + …

n^th term, an = ( 2n + 1) n² = 2n³ + n²

Question 4:

Find the sum to n terms of the series 

Answer:

The given series is 

n^th term, an = 

Adding the above terms column wise, we obtain

Question 5:

Find the sum to n terms of the series 

Answer:

The given series is 5² + 6² + 7² + … + 20²

n^th term, an = ( n + 4)² = n² + 8n + 16

16^th term is (16 + 4)² = 20²2

Question 6:

Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…

Answer:

The given series is 3 × 8 + 6 × 11 + 9 × 14 + …

an = (n^th term of 3, 6, 9 …) × (n^th term of 8, 11, 14, …)

= (3n) (3n + 5)

= 9n² + 15n

Question 7:

Find the sum to n terms of the series 1² + (1² + 2²) + (1² + 2² + 3²) + …

Answer:

The given series is 1² + (1² + 2²) + (1² + 2² + 3² ) + …

an = (1² + 2² + 3² +…….+ n²)

= nn+12n+16=n2n2+3n+16=2n3+3n2+n6=13n3+12n2+16n

Question 8:

Find the sum to n terms of the series whose n^th term is given by n (n + 1) (n + 4).

Answer:

an = n (n + 1) (n + 4) = n(n² + 5n + 4) = n³ + 5n² + 4n

Question 9:

Find the sum to n terms of the series whose n^th terms is given by n² + 2n

Answer:

an = n² + 2n

Consider 

The above series 2, 2², 2³, … is a G.P. with both the first term and common ratio equal to 2.

Therefore, from (1) and (2), we obtain

Question 10:

Find the sum to n terms of the series whose n^th terms is given by (2n – 1)²

Answer:

an = (2n – 1)² = 4n² – 4n + 1