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NCERT Solutions For Class 10 Maths Chapter 5 Arithmetic Progressions

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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

a,a+d, a+2d, a+3d, a+4d, a+5d,.........................................a+(n-1)d

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

$S_n=\frac{n}{2}(2a+(n-1)d)=\frac{n}{2}(first\ term+last\ term)$

where a is the first term, n is the number of terms in the given A.P and d is a common difference.

The NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions- Exercise Solutions

NCERT Solutions for Class 10 Maths - Chapter-wise

Chapter No.	Chapter Name
Chapter 1	Real Numbers
Chapter 2	Polynomials
Chapter 3	Pair of Linear Equations in Two Variables
Chapter 4	Quadratic Equations
Chapter 5	Arithmetic Progressions
Chapter 6	Triangles
Chapter 7	Coordinate Geometry
Chapter 8	Introduction to Trigonometry
Chapter 9	Some Applications of Trigonometry
Chapter 10	Circles
Chapter 11	Constructions
Chapter 12	Areas Related to Circles
Chapter 13	Surface Areas and Volumes
Chapter 14	Statistics
Chapter 15	Probability