NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions: We can see many patterns in nature such as the arrangement of petals of a flower, the pattern of honeycomb, etc. We also follow certain patterns in daily life. For example, Seema puts rupees 1000 into her daughter’s money box when she was one year old and increased the amount by ` 100 every year. Then the pattern will be 1000,1100,1200,...........for 1st, 2nd, 3rd,................years. In NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions, we will discuss the patterns in which succeeding terms are obtained by adding a fixed number to the preceding terms. Also in NCERT Solutions for Class 10 Maths Chapter 5 we will study how to find their general term and the sum of n consecutive terms in the pattern mentioned above, and use this knowledge in solving some daily life problems.
The above-mentioned pattern is known as Arithmetic Progression.
A general pattern of arithmetic Progression gave in NCERT Solutions of this chapter is given below
Where a is known as the first term, d is the common difference and nth term is a+(n-1)d
It is not necessary that the first term should be taken as a. In certain problems, we take terms of A.P as a-d, a, a+d.........
Let's see an example related to the above concept from NCERT Solutions for Class 10:
Q) In an AP with positive common difference sum of the first three terms is 24 and the product of the first 3 terms is 312. Find the first term and common difference.
Solution: if we take a,a+d and a+2d as the terms then the sum=3a+3d product will involve cube of a and calculation will be lengthy. Instead, if we take the first three terms as a-d,a+d,a+2d then,
sum=a-d+a+a+d=3a and given 3a=24 there for a =8
product =(a-d)a(a+d)=(8-d)(8+d)8 =8(64-d2)
Given product =312
therefor
8(64-d2)=312 implies 64-d2=39 implies d2=25, there for d=+5 (d= positive: mentioned in the question) and first term is a-d=8-5=3
The main topics of NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions are listed below.
5.1 Introduction
5.2 Arithmetic Progressions
5.3 nth Term of an AP
5.4 Sum of First n Terms of an AP
The sum of first n terms is given by
where a is the first term, n is the number of terms in the given A.P and d is a common difference.
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression- Exercise 5.1
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression- Exercise 5.2
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression- Exercise 5.3
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression- Exercise 5.4
Chapter No. |
Chapter Name |
Chapter 1 |
|
Chapter 2 |
|
Chapter 3 |
|
Chapter 4 |
|
Chapter 5 |
|
Chapter 6 |
|
Chapter 7 |
|
Chapter 8 |
|
Chapter 9 |
|
Chapter 10 |
|
Chapter 11 |
|
Chapter 12 |
|
Chapter 13 |
|
Chapter 14 |
|
Chapter 15 |
Q : 1 In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
(i) The taxi fare after each km when the fare is for the first km and
for each additional
.
Q : 12 Find the sum of the first positive integers divisible by
.
Q : 3 For the following APs, write the first term and the common difference:
(ii)