# Xam Idea Class 10 Maths Chapter 5 Solutions: Arithmetic Progressions

Xam Idea Class 10 Maths Solutions for Chapter 5 ‘Arithmetic Progressions’ is a complete guide for your exam preparation. All the solutions are designed in accordance with the latest guidelines prescribed by CBSE and NCERT. They not only help you in getting good marks but they also increase and enhance your knowledge. All the Xam Idea Solutions will help you to practice the topics of the chapter in a beneficial and productive way. The chapter elaborates the meaning of arithmetic progression and its representation, how to find the n^{th} term of an AP, how to make an AP or find its first term and common difference. All the solutions are formulated in a simple and organised format covering all these topics.

Xam Idea Class 10 Maths Solutions for Arithmetic Progressions cover 58 questions. The exercise has been divided into 6 sections where you can get practice questions as per the latest CBSE exam pattern. The exercises contain a variety of questions such as very short answer type questions, long answer type questions, HOTS (higher-order thinking skills) and value-based questions. All the questions are based on the important and crucial topics of the chapter that cover the entire syllabus of board exams. Xam Idea Class 10 Maths HOTS solutions are very helpful in preparing for different competitive exams.

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## Important Topics for Xam Idea Class 10 Maths Solutions Chapter 5: Arithmetic Progression (AP)

The chapter revolves around AP and explains what is an AP, what is the difference between a series and AP, different elements that are responsible for making an AP. It also includes the topics such as the first term, last term, common difference, nth term, the sum of two all the terms of two APs, the sum of the nth term of an AP and how to form an AP from the statement. It also covers the general term of AP, finite and infinite AP, the sum of first n natural numbers etc.

**Introduction**

- A sequence is a finite or infinite list of numbers following a certain pattern. For example, 1,2,3,4,5……… is the sequence of natural numbers.
- A series is the sum of the elements in the corresponding sequence. For example, 1+2+3+4+5… is the series of natural numbers. Each number in a sequence or series is called a term.
- A progression is a sequence in which the general term can be expressed using a mathematical formula.
- An arithmetic progression is a progression in which the difference between two consecutive terms is constant. For example, 2,5,8,11,14… is an arithmetic progression.
- The difference between two consecutive terms in an AP is known as the common difference. It is a constant number applicable for the whole series.
- If the common difference is positive then the AP is increasing. If the common difference is zero then the AP is constant and if the common difference is negative the AP is decreasing.
- The AP in which the number of terms is finite then it is called Finite AP. For example, 1,2,3,4 is a series with only 4 terms.
- If the number of terms in an AP is infinite then it is called Infinite AP. For example, 4,5,6,7,8…up to n is an infinite series.

**General Term And Sum Of An AP**

- The nth term of an AP is given by Tn=a+(n-1)d where a is the first term, d is a common difference and n is the nth term of the AP.
- The general form of AP is a+d, a+2d, a+3d,a+4d……. Where a is the first term and d is a common difference.
- The sum of n terms is given by Sn=n/2(2a+(n-1)d) where a is the first term, d is a common difference and n is the number of terms.
- The arithmetic mean is the simple average of a given set of numbers. It is given by the sum of the terms/number of terms.
- The sum of first n natural numbers is given by Sn=n(n+1)/2.

### Exercise Discussion Of Xam Idea Class 10 Maths Solutions Chapter 5: Arithmetic Progression

**Very Short Answer Type Questions**

This section includes 8 very short answer type questions such as you have the AP and you have to find the nth term of the AP. It also contains questions like the first term and common difference will be given and you have to find the 10th term.

**Short Answer Type Question-I**

This section contains 14 questions in all and you have to find the first term, last term, the common difference with the help of hints given. It also covers the statement type questions in which you have to make the AP.

**Short Answer Type Questions-II**

This section covers the total number of 16 questions. In this you will have the terms and you have to find the number of that term or you have the number of terms and you have to check whether the term is zero or not.

**Long Answer Questions**

Overall, it contains 7 questions in which you have to let the AP and further find the AP with the clues that are given in the question. It also includes the questions in which you have to find the sum of terms of AP through the formulas.

**Higher-Order Thinking Skills **

This section covers 8 questions in total and is kind of confusing questions. In this, you will face questions like find the sum of the first 15 multiples of 8 or find the sum of all two-digit numbers which when divided by 3 gives one as a remainder.

**Value-Based Questions**

This section has 5 questions in which you have to make the Ap and solve that with the help of some basic or simple value from your life and you have to give advice according to the question.

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