Chapter 9 Sequences and Series Ex 9.4 Solutions
Question - 1 : - Find the sum to n terms of each of the series in Exercises 1 to 7.
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
Answer - 1 : -
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 nterms of the series can be expressed as
Question - 2 : - 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …
Answer - 2 : -
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 nterms of the series can be expressed as
Question - 3 : - 3 × 12 + 5 × 22 +7 × 32 + …
Answer - 3 : -
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 nterms of the series can be expressed as
Question - 4 : - Find the sum to n terms of the series
Answer - 4 : -
Question - 5 : - Find the sum to n terms of the series 52 +62 + 72 + … + 202
Answer - 5 : -
Given series is 52 +62 + 72 + … + 202
It’s seen that,
nth term, an = ( n +4)2 = n2 + 8n + 16
Then, the sum of nterms of the series can be expressed as
Question - 6 : - Find the sum to n terms ofthe series 3 × 8 + 6 × 11 + 9 × 14 +…
Answer - 6 : -
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 nterms of the series can be expressed as
Question - 7 : - Find the sum to n terms of the series 12 +(12 + 22) + (12 + 22 +32) + …
Answer - 7 : -
Given series is 12 +(12 + 22) + (12 + 22 +32 ) + …
Finding the nth term,we have
an = (12 + 22 +32 +…….+ n2)
Now, the sum of nterms of the series can be expressed as
Question - 8 : - Find the sum to n terms of the series whose nth termis given by n (n + 1) (n + 4).
Answer - 8 : -
Given,
an = n (n + 1)(n + 4) = n(n2 + 5n +4) = n3 + 5n2 + 4n
Now, the sum of nterms of the series can be expressed as
Question - 9 : - Find the sum to n terms ofthe series whose nth terms is given by n2 +2n
Answer - 9 : -
Given,
nth termof the series as:
an = n2 + 2n
Then, the sum of nterms of the series can be expressed as
Question - 10 : - Find the sum to n terms of the series whose nth termsis given by (2n – 1)2
Answer - 10 : -
Given,
nth termof the series as:
an = (2n – 1)2 =4n2 – 4n + 1
Then, the sum of nterms of the series can be expressed as
