NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression Exercise 5.2

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NCERT Class 10 Maths Solutions for Chapter 5 Arithmetic Progression Ex 5.2

The NCERT Solutions for Class 10 Maths Chapter 5 Exercise 5.2 has been prepared in detail by the subject matter experts at Vedantu. The experts have a lot of grasp on this topic, having taught students for many years. AP is an important topic and students will have to develop its basics to be able to do well in the higher classes. The Ex 5.2 Class 10 Maths NCERT Solutions are of importance and is used in higher education as well. If students build their foundations strong in the junior classes, it lets them do well in the boards as well as perform well in the competitive examinations. The PDF version of NCERT Maths Class 10 Chapter 5 Exercise 5.2 is easy to assess, and all that the students have to do is to download the CBSE Class 10 Maths PDF and refer to it when needed. Students can also download NCERT Solutions Class 10 Science PDF for free from Vedantu.

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2

The best part about the Maths 5.2 Class 10 PDF solution is that it can be downloaded for free. All that the students need is an internet connection to download the NCERT solutions for Class 10 Maths EX 5.2 from the main website of Vedantu. Once downloaded, they can refer to the solution on the go. The 10 Class Math exercise 5.2 solution can be referred to just before the examination. Students can also print a hard copy of the Exercise 5.2 Maths Class 10 solutions if they want to keep it handy always.

NCERT Solutions for Class 10 Maths Exercise 5.2 – Arithmetic Progression

5.2 Arithmetic Progression

Be it in nature or any company figures you will notice that data follows a particular pattern. This could be anything be it the pattern of the petals on a sunflower or the order in which the honeybee comb is designed and formed. When you notice a pattern you will notice that there is a formula between the succeeding and preceding term. It could be that the succeeding and the preceding terms are the sums or the difference of some number that follows a particular ratio. There are many such progressions when you go about studying mathematics. A very important one among them is the arithmetic progression.

Arithmetic progression or AP is a series where a pattern is formed when the succeeding term is formed by adding a particular number to the previous value. For example, if the first term is ‘a’ then and the next term is ‘a+d’, the number after that is ‘a+2d’ and then ‘a+3d’ and so on. When you notice a pattern of numbers that has d as the common difference between its two consecutive numbers, then this is an arithmetic progression.

nth term of an AP

If you have been given a series and you figure out that it is in an arithmetic progression, then how do you go about finding out what could be the nth term of this series. This section helps students to derive the formula for the nth term of an AP series that in turn lets you find the nth term of any AP series.

The nth term of the AP series is calculated as: a(n) = a+ (n-1)d

Here ‘a’ is the first term of the series, ‘n’ is the term that you wish to find out, and ‘d’ is the common difference between two successive terms in the AP series. Students need to remember this formula and then need to find out what the n and the d values are. Apply it in the formula and get the nth term of the AP series.

Sum of the first N terms of an AP

The section explains how on getting an AP series; you can go ahead and find the sum of n terms of an AP series. This is important to know because it makes no sense to use a calculator and add each term of the AP series to find out its sum. The section helps students to derive the formula of the n terms of an AP, and this formula can be used to find out the summation. All that the student needs to do is to remember the formula and then to apply the value correctly to the formula to get the right answers.

The sum of n terms an AP series is calculated as:

S = (n/2) (2a+ (n-1) d)

Also if you have an AP series where the first number is 1, then the sum of n terms of the particular AP series with the first number as one is calculated as:

S = (n/2) (a+1)

Summary

The section summarizes all the important formulas and explains how an AP pattern is formed and how to calculate the nth term and the sum of n terms of an AP series.

Key Features of NCERT Solutions for Class 10 Maths Exercise 5.2

The key features of Class 10 Maths Ex 5.2 solutions are:

The concept has been explained concisely and solves all the doubts that the student may have when he goes through the chapter.
The Class 10 Maths Exercise 5.2 Solutions problems are solved through various approaches that let students tackle all kinds of questions on this topic.
The language used in Exercise 5.2 Class 10 Solutions is easy, which means that anyone can go through these solutions and understand the topic.

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FAQ (Frequently Asked Questions)

1. Where can you observe the AP series and its application in real life?

Suppose that you have got a new job and you have been told that you will be paid an amount A in the first year. You are then told, each year you will be given an increment of D. This will let you calculate your salary in the 2nd, 3rd, fourth and the consecutive years. This is nothing but an AP series which has A as its first value and D is a common difference. To know what your salary will be in the n years, all that you need to do is to apply the formula of the nth term. This will let you calculate what your salary will be in the nth year of your service.

2. Where can we use the sum of the AP series in real life?

Let us assume that your mother used to put Rs 50 in your piggy bank in year 1. Each year she puts in Rs 50 more than the previous year in your piggy bank on your birthday. So while you have Rs 50 in year 1. The second-year your mother puts in Rs 100 and Rs 150 in the third year and so on. You want to calculate what will be the total amount of money that you will have in your piggy bank once you reach 21 years of age. This is where you apply the formula of the sum of n terms in the AP series. It lets you calculate the total summation of the amount in your piggy bank for year 1 to year 21.