NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2
Get Free NCERT Solutions for Class 10 Maths Chapter 5 Ex 5.2 . Arithmetic Progressions Class 10 Maths NCERT Solutions are extremely helpful while doing your homework. Exercise 5.2 Class 10 Maths NCERT Solutions were prepared by Experienced Garry Academy Teachers. Detailed answers of all the questions in Chapter 5 Maths Class 10 Arithmetic Progressions Exercise 5.2 are provided in NCERT TextBook.
Topics and Sub Topics in Class 10 Maths Chapter 5 Arithmetic Progressions:
Section Name | Topic Name |
5 | Arithmetic Progressions |
5.1 | Introduction |
5.2 | Arithmetic Progressions |
5.3 | Nth Term Of An AP |
5.4 | Sum Of First N Terms Of an AP |
5.5 | Summary |
Board | CBSE |
Textbook | NCERT |
Class | Class 10 |
Subject | Maths |
Chapter | Chapter 5 |
Chapter Name | Arithmetic Progressions |
Exercise | Ex 5.2 |
Number of Questions Solved | 20 |
Category | NCERT Solutions |
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Exercise 5.2
Ex 5.2 Class 10 Maths Question 1.
Fill in the blanks in the following table, given that a is the first term, d is the common difference and the nth term of the AP:
Solution:
Ex 5.2 Class 10 Maths Question 2.
Choose the correct choice in the following and justify:
(i) 30th term of the AP: 10, 7, 4, …, is
(a) 97
(b) 77
(c) -77
(d) -87
(ii) 11th term of the AP: -3,
(a) 28
(b) 22
(c) -38
(d) -48
Solution:
Ex 5.2 Class 10 Maths Question 3.
In the following APs, find the missing terms in the boxes:
Solution:
Ex 5.2 Class 10 Maths Question 4.
Which term of the AP: 3, 8, 13, 18, …, is 78?
Solution:
Ex 5.2 Class 10 Maths Question 5.
Find the number of terms in each of the following APs:
(i) 7, 13, 19, …, 205
(ii) 18, 15
Solution:
Ex 5.2 Class 10 Maths Question 6.
Check, whether -150 is a term of the AP: 11, 8, 5, 2, ….
Solution:
Ex 5.2 Class 10 Maths Question 7.
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Solution:
Ex 5.2 Class 10 Maths Question 8.
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Solution:
Ex 5.2 Class 10 Maths Question 9.
If the 3rd and the 9th term of an AP are 4 and -8 respectively, which term of this AP is zero?
Solution:
Ex 5.2 Class 10 Maths Question 10.
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Solution:
Ex 5.2 Class 10 Maths Question 11.
Which term of the AP: 3, 15, 27, 39, … will be 132 more than its 54th term?
Solution:
Ex 5.2 Class 10 Maths Question 12.
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Solution:
Ex 5.2 Class 10 Maths Question 13.
How many three-digit numbers are divisible by 7?
Solution:
Ex 5.2 Class 10 Maths Question 14.
How many multiples of 4 lie between 10 and 250?
Solution:
Ex 5.2 Class 10 Maths Question 15.
For what value of n, the nth term of two APs: 63, 65, 61,… and 3, 10, 17,… are equal?
Solution:
Ex 5.2 Class 10 Maths Question 16.
Determine the AP whose 3rd term is 16 and 7th term exceeds the 5th term by 12.
Solution:
Ex 5.2 Class 10 Maths Question 17.
Find the 20th term from the last term of the AP: 3, 8, 13, …, 253.
Solution:
Ex 5.2 Class 10 Maths Question 18.
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Solution:
Ex 5.2 Class 10 Maths Question 19.
Subba Rao started work in 1995 at an annual salary of ₹ 5000 and received an increment of ₹ 200 each year. In which year did his income reach ₹ 7000 ?
Solution:
Ex 5.2 Class 10 Maths Question 20.
Ramkali saved ₹ 5 in the first week of a year and then increased her weekly saving by ₹ 1.75. If in the nth week, her weekly saving become ₹ 20.75, find n.
Solution:
Class 10 Maths Arithmetic Progressions Mind Maps
Arithmetic Progression (AP)
Consider
(i) 1, 2, 3, 4, ……
(ii) 3, 3, 3, 3, …..
(i) and (ii) are the sequence of numbers, each number in these sequences is called a term.
An arithmetic progression (AP) is a sequence of numbers in which each term is obtained by adding a fixed number ‘d’ to the preceeding term, except the first term.
The fixed number is called the common difference. It can be positive, negative or zero.
Any Arithmetic progression can be represented as :
a, a + d, a + 2d, a + 3d,…..
where ‘a’ is the first term and ‘d’ is the common difference. Arithmetic progressions which does not have a last term are called Infinite Arithmetic Progression. e.g.:
6, 9, 12, 15,…….
The formula for common Difference (d)
A sequence of numbers a1, a2, a3…. is an AP if the difference a2 – a1, a3 – a2, a4 – a3…. gives the same value, i.e. if ak+1 – ak is the same for different values of k. The difference (ak+1 – ak) is called common difference (d). Here ak+1 and ak are the (k + 1)th and kth terms respectively.
∴ d = a2 – a1 = a3 – a2 = a4 – a3
nth Term (or General Term) of an Arithmetic Progressions
In an AP, with first term ‘a’ and common difference d, the nth term(or the general term) is given by,
an = a + (n – 1)d
Note that an AP can be finite or infinite according to as the number of terms are finite or infinite.
If there are m terms in an AP then am is the last term and is sometimes denoted by ‘l’.
Sum of the FIRST ‘n’ Terms of an A.P.
(i) The sum of the first n terms of an A.P. is given by
where a is the first term and d is the common difference
(ii) If l is the last term of the finite A.P. say the nth term, then the sum of all terms of the A.P. is given by,
Note that sum of first n positive integers is given by
Arithmetic Mean Between Two Numbers
If a, b, c are in AP. Then b is called the arithmetic mean of a and c and is given by
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