NCERT Solutions For Class 10 Mathematics Chapter 5 Arithmetic Progressions
Mathematics is one subject that most students find difficult. The only way to actually score good marks in Mathematics is to practice solving as many problems as one can. That is why students find NCERT Solutions For Class 10 Mathematics Chapter 5 by Extramarks really useful in their preparation. If students ever get stuck on any of the exercise questions, they can always refer to these solutions. These are also great resources for completing assignments and for last-minute revision.
Access NCERT Solutions for Mathematics Chapter 5 – Arithmetic Progression
Chapter 5 of Class 10 Mathematics NCERT textbook introduces students to Arithmetic Progressions, which are nothing but lists of numbers where each term, except the first term, can be derived by adding or subtracting a fixed number to its preceding term. These are really useful to express patterns that we see in our daily lives and in nature. The chapter further discusses the different types of Arithmetic Progressions, the sum of Arithmetic Progressions, deriving a general formula for the nth term of an Arithmetic Progression, and much more.
What is Arithmetic Progression?
An Arithmetic Progression is a series of numbers where each number can be derived from its predecessor by adding or subtracting a fixed number. For example, consider the series of numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Here, each term can be derived from its predecessor by adding 1 to it.
The fixed difference between the terms of an AP is called the common difference. In the above example, the common difference is 1.
NCERT Solutions for Class 10 Mathematics
Extramarks provides detailed NCERT Solutions for Class 10 Mathematics. Since the only way to get good at Mathematics is to solve problems, these solutions can be very useful for students. Extramarks provides detailed solutions to the questions given in all of the NCERT Mathematics textbooks chapters listed below:
- 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
The General Form of an Arithmetic Progression
The general form of an AP can be expressed as follows:
A, A + d, A + 2d, A + 3d,….
Here, A is the first term and d is the common difference.
| Position Of Terms |
Representation of terms |
Value of Terms |
| 1 |
a1 |
A=a+(1-1) d |
| 2 |
a2 |
A+d=a+(2-1) d |
| 3 |
a3 |
A+2d=a+(3-1) d |
| 4 |
a4 |
A+3d=a+(4-1) d |
| . |
|
|
| . |
|
|
| . |
|
|
| . |
|
|
| N |
An |
A+(n-1)d |
The Formulas
There are some essential formulae that students will need to solve problems related to Arithmetic Progressions. These formulae have been listed below:
- Arithmetic Progression’s nth Term (AP)
Students will face many problems related to this chapter where they will be expected to calculate the nth term of an Arithmetic Progression. The formula to calculate the nth term of an AP is shown below:
An = a + (n – 1) d
Here,
a= The initial term
d= The difference value
n= the number of terms
An= the nth term
Consider the following problem. Calculate the 15th term in the AP: 1, 2, 3, 4, 5 …
Here, we are supposed to calculate the 15th term. So, the value of n is 15. The first term, a, is 1 and the common difference is also 1. Using the formula to calculate the nth term of an AP, the 15th term can be calculated as follows:
A15 = 1 + (15 – 1) 1 = 1 + 14 = 15.
- The Sum of the First n Terms
Another common type of problem that students will face related to Arithmetic Progressions is to calculate the sum of the first n terms of a given AP. The formula to do so is shown below:
S = (n / 2)*(2a+(n−1)d)
Here,
n is the number of terms
a is the first term in the AP
d is the common difference
Here, using the formula the nth term of an AP, we can further simplify this expression to the one shown below:
S = (n/2)*(a+An)/2
Here,
An is the nth term of the AP
Also, if the nth term is actually the last term of the AP, then the formula is further simplified to the following:
S = n / 2 (first term + last term)
We’ve also included all of the crucial formulas in this chapter in a table for easy reference.
| General Form of AP |
A, a + d, a + 2d, a + 3d, a + 4d, …, a + nd |
| The nth term of AP |
An = a + (n – 1) x d |
| Sum of n terms in AP |
S= (n/2)*(2a + (n – 1)d) |
| Sum of all terms in a finite AP with the last term as I |
(n/2)*(a + I) |
Why should students refer to NCERT Solutions from Extramarks?
Extramarks is committed to supporting students in every way. . We work to ensure that students can manage their academic and personal responsibilities more efficiently. The NCERT Solutions provides solutions for the Class 10 Chapter by Extramarks will help students cross-check their answers or even get the right answers to the textbook questions. Additionally, students will also get an idea of how to attempt a question in the right manner.
The Benefits of Referring to NCERT Solutions Mathematics
NCERT Solutions for Class 10 Mathematics Chapter 5 from Extramarks is a useful resource that will definitely help students to step up their preparation. Here are some of the benefits:
- All the answers are written following the CBSE guidelines. When students study from it, they will get an edge over their peers.
- Subject matter experts write these solutions giving utmost importance to accuracy so that students are able to understand every concept and answer any question easily.
- All the answers are written in a step-by-step manner, ensuring students do not have any difficulty understanding how the answer is derived. This encourages the students to master the topic and increases their confidence in achieving a higher grade