ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Solutions Chapter-10. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-1,  Exe-2, Exe-3 Exe-4, Exe-5, Exe-6, Exe-7, Exe-8, Exe-9, Exe-10 and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Class: 11th
Subject: Mathematics
Chapter  : Ch-10 Sequences and Series of Section -A
Board ISC
Writer ML Aggarwal
Publications APC Arya Publications 2020-21

-: Select Topics :- 

Exe-10.1,

 Exe-10.2,

 Exe-10.3,

 Exe-10.4,

 Exe-10.5,

 Exe-10.6,

 Exe-10.7,

 Exe-10.8,

 Exe-10.9,

 Exe-10.10,

Chapter Test


ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Sequences and Series 

The different numbers occurring in any particular sequence are known as terms. The terms of a sequence are denoted by

a1, a2, a3,….,an

If a sequence has a finite number of terms then it is known as a finite sequence. A sequence is termed as infinite if it is not having a definite number of terms. The nth term of an AP is given by

a + (n-1) d.

Between any two numbers ‘a’ and ‘b’, n numbers can be inserted such that the resulting sequence is an Arithmetic Progression. A1, A2, A3,……,An be n numbers between a and b such that a, A1 , A2 , A3,……,An, b is in A.P.

Here, a is the 1st term and b is (n+2)th term. Therefore,

b = a + d[(n + 2) – 1] = a + d (n + 1).

Hence, common difference (d) = (b-a)/(n+1)

Now, A1= a+d= a+((b-a)/(n+1))

A2= a+2d = a + ((2(b-a)/(n+1))

An = a+nd= a + ((n(b-a)/(n+1))}

The nth term of a geometric progression is given by a= arn-1

Sum of nth term:

Sn = n/2 [2a + (n-1)d]

where n = number of terms, a = first term and d = common difference

Sequence
A succession of numbers arranged in a definite order according to a given certain rule is called sequence. A sequence is either finite or infinite depending upon the number of terms in a sequence.

Series
If a1, a2, a3,…… an is a sequence, then the expression a1 + a2 + a3 + a4 + … + an is called series.

Progression
A sequence whose terms follow certain patterns are more often called progression.

Arithmetic Progression (AP)
A sequence in which the difference of two consecutive terms is constant, is called Arithmetic progression (AP).

Properties of Arithmetic Progression (AP)

If a sequence is an A.P. then its nth term is a linear expression in n i.e. its nth term is given by An + B, where A and S are constant and A is common difference.

nth term of an AP : If a is the first term, d is common difference and l is the last term of an AP then

  • nth term is given by an = a + (n – 1)d.
  • nth term of an AP from the last term is a’n =an – (n – 1)d.
  • an + a’n = constant
  • Common difference of an AP i.e. d = an – an-1,∀ n > 1.

If a constant is added or subtracted from each term of an AR then the resulting sequence is an AP with same common difference.

If each term of an AP is multiplied or divided by a non-zero constant, then the resulting sequence is also an AP.

If a, b and c are three consecutive terms of an A.P then 2b = a + c.

Any three terms of an AP can be taken as (a – d), a, (a + d) and any four terms of an AP can be taken as (a – 3d), (a – d), (a + d), (a + 3d)


Exe-10.1

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

Give an example of a sequence which is not a progression.

Question 2:

Which terms of the sequence given by ……………….

Question 3:

…………………..

……………………..

…………………….

Question 12:

First term of a sequence is 1 and the (n + 1) th term is obtained by adding …………………….. term of the sequence.


Exe-10.2

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

Find the :

(i) Eighteenth term ………………..

……………………..

Question 2:

Write the first four terms of each of the following sequence :

(i) an A.P. with ………………

………………….

Question 3:

………………………

……………………….

………………………..

Question 27:

If log3 2, log3 (2x – 5 ) and log3 (2x – 7/2) are in A.P., determine the value of x.


Exe-10.3

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

Find the sum :

(i)………….

………………

Question 2:

Find the sum of an A.P. of

(i) 25 terms whose nth ………………

(ii) 19 terms whose ……………………

Question 3:

……………………

…………………..

…………………..

Question 26:

Kumar buys a Maruti car for ……………… what will the car cost him ?


Exe-10.4

 Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

(i) Find the arithmetic ………………….

(ii) Insert two arithmetic …………………

(iii) Insert 3 ……………….

Question 2:

If S is the sum of  n arithmetic ……………………… find the value of S/A.

Question 3:

………………….

…………………..

…………………..

Question 8:

There are n arithmetic means between ……………….. 1 : 3 . Find n.


Exe-10.5

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

Can 0 be a term of a geometric progression ?

Question 2:

(i) Find the next term of the sequence …………..

(ii) Find the next terms ………..

……………..

Question 3:

……………………….

……………………….

…………………………..

Question 32:

The length of the sides of a triangle form a G.P. If the perimeter of the triangle is 37 cm and the ………………. other two sides.


Exe-10.6

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

Find the sum of :

(i) 20 term ……………..

…………………..

Question 2:

Find the sum of the first 10 terms of the geometric series

………………

Question 3:

……………………

……………………

……………………

Question 31:

The inventor of chessboard was a very clever man . He ……………………. to be given ?


Exe-10.7

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

(i) Insert 2 number between 3 and 81  so that resulting sequence is G.O.

(ii)  Insert 3 geometric ……………

(iii) Insert 4 geometric means ……………

Question 2:

If the fourth term of a ………… 7 terms.

Question 3:

………………………

………………………

………………………

Question 13:

Find the minimum value of …………………….. x ∈ R.


Exe-10.8

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

Sum to infinity the following series :-

(i)…………..

……………….

Question 2:

Sum to n terms the following series :

(i)……………….

(ii)………………

………………….

Question 3 :

……………………..

……………………..

………………………

Question 5:

(i) If the sum to infinity of the series …………………… find r.

(ii) If the sum ……………………


Exe-10.9

 Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

Find the 20th terms of the series ……………………….

Question 2:

If 1 + 2 + 3 + ……………….. value of n.

Question 3:

………………………

……………………….

……………………….

Question 13:

Find the n th term and the sum of n ……………………..


Exe-10.10

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

If a1, a2, ………………. show that ……….

Question 2:

Certain number appear in both the sequence ………………  in the both the sequence .

Question 3:

……………………..

……………………..

,……………………..

Question 9:

Sum to infinity the following series :

(i) ………………….

(ii)…………………..


Chapter Test

ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding Ch-10

Question 1:

If 10 th term of an A.P. is 52 and its 16th term is 82, find the 32nd term.

Question 2:

In an A. P., if the third terms is p and fourth terms is q, find the 10- th and n th terms .

Question 3:

……………………….

………………………..

………………………….

Question 30:

Find the n th terms and the sum of n terms of the series :

………………………..

-: End of Sequences and Series ISC Class-11 ML Aggarwal Maths Understanding Chapter-10 Solution :-

Return to :-  ML Aggrawal ISC Class-11 APC Understanding Maths Solutions


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18 thoughts on “ML Aggarwal Sequences and Series ISC Class-11 Maths Understanding”

    • dear student / well wisher / Teacher
      the previous version of 2020-21 has been removed because council has decided to start new session from 1st April Therefore we are upgrading the solutions of 2021-22 editions
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      team icsehelp

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