**NCERT Solutions of Class 11 Maths Exercise 9.1 – Sequences and Series**

NCERT Solutions of class 11 maths exercise 9.1 of chapter 9-‘Sequences and series’ are the solutions of unsolved question exercise 9.1 of chapter 9 of class 9 NCERT textbook prescribed by CBSE a reputed board for school education.All questions of exercise 9.1 of chapter 9 of the maths NCERT textbook are solved by an expert of maths by a step by step method, so every student can understand the solutions quickly.

In class 10 you have studied one part of Sequences and Series, the chapter ‘Arithmetic Progression’, now in class 11 you will study it in more advance with other important series geometrical progression and other complex series.

**NCERT Solutions For Class 11 Maths of Chapter 9 Sequences and Series**

**Exercise 9.2 – Sequence and Series**

**Exercise 9.3 – Sequence and Series**

**Exercise 9.4 – Sequence and Series**

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**NCERT Solutions of exercise 9.1 ‘ Sequences and Series**

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**Q1.Write the first 5 terms of the sequence whose n the term is a _{n} = n(n +2).**

Ans. The n the term of the series is given to us = n(n + 2)

The first term(n=1) of the series = 1(1 +2) = 3

Second term(n =2) of the series = 2(2 + 2) = 8

Third term of the series(n =3) = 3(3 + 2) = 15

Fourth term of the series (n =4) = 4( 4 +2) =24

Fifth term of the series (n =5) = 5(5 + 2) = 35

**Q2.Write the first 5 terms of the sequences whose n the term is **

Ans. The n the term given to us is

Substituting n by the first 5 numbers 1,2,3,4 and 5, we will get first 5 terms of the sequences.

Hence the first 5 terms of the sequences are 1/2,2/3,3/4, 4/5 and 5/6

**Q3. Write the first five terms of the sequences whose n the term is a _{n} = 2^{n}**

Ans. We are given the n the term

a_{n} = 2^{n}

Substituting n by first numbers, we will get first 5 terms

a_{1} = 2^{1}= 2, a_{2} = 2^{2} = 4, 2^{3} = 8, 2^{4} =16, 2^{5} = 32

Hence first 5 terms of the sequences are 2,4,8,16 and 32.

**Q4.Write the first five terms of the sequences whose n the term is**

Ans. We are given the n the term

Substituting n by first 5 numbers, 1,2,3,4 and 5 we will get first 5 terms

Hence first 5 terms of the sequences are -1/6,1/6, 1/2,5/6 and 7/6

**Q5. .Write the first five terms of the sequences whose n the term is a _{n} = (-1)^{n-1}5^{n+1}**

Ans.We are given the n the term, a_{n} = (-1)^{n-1}5^{n+1}

Substituting n by first 5 numbers, 1,2,3,4 and 5 we will get first 5 terms

a_{1} = (-1)^{1-1}5^{1+1},=(-1)^{0}5^{²} = 5² = 25

a_{2} = (-1)^{2-1}5^{2+1},=(-1)^{1}5³ = -1×5³ = -125

a_{3} = (-1)^{3-1}5^{3+1} =(-1)^{2}5^{4} = 625

a_{4} = (-1)^{4-1}5^{4+1} =(-1)^{3}5^{5} = -3125

a_{5}= (-1)^{5-1}5^{5+1} =(-1)^{4}5^{6} = -15625

Hence first 5 terms of the sequences are

**Q5. .Write the first five terms of the sequences whose n the term is**

Ans.We are given the n the term

Substituting n by first 5 numbers, 1,2,3,4 and 5 we will get first 5 terms

Hence first 5 terms of the sequences are 3/2, 9/2, 21/2, 21 and 75/2

**Q7. Find 17 the and 24 term in the following sequence whose n th term is a _{n} = 4n -3**

Ans. We are given the n th term, a_{n} = 4n -3

Substituting n = 17 and n =24 in the n th term of the sequences

a_{17} = 4×17 -3=68-3=65

a_{24} = 4×24 -3=96-3=93

**Q8.Find the seventh term in the following sequence whose n th term is**

Ans.We are given the n th term of the sequence

Substituting n = 7

**Q9..Find the nine th term in the following sequence whose n th term is**

**a _{n} = (-1)^{n-1}n^{3}**

Ans. We are given the n th term of the sequence

a_{n} = (-1)^{n-1}n^{3}

Substituting n = 9

a_{9}= (-1)^{9-1}9^{3},=1X729 = 729

**Q10.Find the 20 th term in the following sequence whose n th term is**

Ans. We are given the n th term of the sequence

Substituting n = 20

**Q11.Write the first 5 terms of the following sequence and obtain the corresponding series.**

**a _{n} = 3a_{n-1} +2 for all n >2.**

Ans. We are given a_{1}=3 and a_{n} = 3a_{n-1} +2 for all n >2

The n th term of the sequence is

a_{n} = 3a_{n-1} +2 for all n >2

Substituting n = 2,3,4,5 we have

a_{2} = 3a_{2-1} +2 = 3a_{1} +2=3×3+2=11

a_{3} = 3a_{3-1} +2 = 3a_{2}+2=3×11+2=35

a_{4} = 3a_{4-1} +2 = 3a_{3}+2=3×35+2=107

a_{5} = 3a_{5-1} +2 = 3a_{4}+2=3×107+2=323

First 5 terms of the sequence are 3,11,35,107 and 323

**Try question number from 12 to 14**

**Q12.Write the first 5 terms of the following sequence and obtain the corresponding series.**

Ans. We are given the first and nth term of the sequence

Substituting n = 2,3,4,5 we have

The second term of the sequence

Therefore first 5 terms of the series are -1,-1/2,-1/6,-1/24 and -1/120

**Q13Write the first 5 terms of the following sequence and obtain the corresponding series.**

**a _{1} = a_{2}**=2,

**a**

_{n }= a_{n-1}– 1, n≥ 2Ans. Given :**a _{1} = a_{2}**=2,

**a**

_{n }= a_{n-1}– 1Then , a_{3 }= a_{2 }– 1 = 2 – 1 = 1

a_{4} = a_{3 }– 1 = 1 – 1 = 0

a_{5 }= a_{4 }– 1 = 0 – 1 = -1

Thus , the first five terms of the sequence are 2 ,2 ,1 ,0 and -1

The corresponding series is

2 + 2 + 1 + 0 +(- 1)+…

**Q14.The Fibonacci sequence is defined by**** **

Ans.Given,

a_{3 }= a_{2 }+ a_{1 }= 1 + 1 = 2

a_{4} = a_{3 }+ a_{2 } = 2 + 1 = 3

a_{5 }= a_{4 }+ a_{3 } = 3 + 2 = 5

Thus ,

For n = 1,2,3,4 and 5 the sequence is given as following

For n =1

For n =2

For n=3

For n= 4

For n= 5

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