# NCERT Solutions For Class 10 Maths Chapter 5 Arithmetic Progressions

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.

## 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

## NCERT Solutions for Class 10 - Subject Wise

 NCERT Solutions for Class 10 Maths NCERT Solutions for Class 10 Science

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