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
Study notes of Maths and Science NCERT and CBSE from class 9 to 12
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≥ 2
Ans. Given :a_{1} = a_{2}=2, a_{n }= a_{n-1} – 1
Then , 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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