NCERT Solutions for Class 10 – Complete Chapter-wise Study Material
5. Arithmetic Progressions is one of the most important chapters in the Class 10 Mathematics English NCERT Solutions curriculum. This chapter plays a significant role in helping students build a strong conceptual foundation while preparing for school examinations, class tests, unit tests, half-yearly examinations, annual examinations, and CBSE board assessments. The chapter has been carefully designed according to the latest NCERT syllabus, making it an essential part of every student's study plan.
The 5. Arithmetic Progressions - Class 10 Mathematics English NCERT Solutions available on ATP Education explain every question in a simple, accurate, and step-by-step manner. Each answer is prepared according to the latest CBSE guidelines so that students can understand the concepts clearly without confusion. Whether you are completing your homework, revising before examinations, or strengthening your understanding of the subject, these solutions provide reliable academic support throughout your learning journey.
One of the biggest advantages of studying 5. Arithmetic Progressions is that it helps students understand important concepts, definitions, examples, and textbook exercises in an organized way. Instead of memorizing answers, students learn how to develop logical thinking, improve analytical skills, and write well-structured answers in examinations. This chapter also helps improve problem-solving ability and encourages conceptual learning, which is essential for scoring higher marks in school and competitive examinations.
Our Class 10 Mathematics NCERT Solutions cover all textbook questions, important exercise questions, and chapter-wise explanations in English Medium. Every solution is written in easy-to-understand language, allowing students to revise the chapter quickly before examinations. Regular practice of these solutions improves confidence, strengthens subject knowledge, and reduces examination stress.
Students preparing for school assessments should carefully study 5. Arithmetic Progressions because questions from this chapter are frequently asked in objective questions, short answer questions, long answer questions, competency-based questions, and case-study questions. Understanding the concepts explained in this chapter also helps students connect related topics from other chapters, making overall learning more effective and meaningful.
At ATP Education, we continuously update our Class 10 Mathematics English NCERT Solutions according to the latest NCERT textbooks and CBSE curriculum. Students can confidently use these chapter-wise solutions for daily study, homework assistance, quick revision, examination preparation, and self-learning. By studying 5. Arithmetic Progressions thoroughly and practising every question regularly, students can strengthen their concepts, improve writing skills, and achieve better academic performance in both school and board examinations.
5. Arithmetic Progressions - Class 10 Mathematics English NCERT Solutions
5. Arithmetic Progressions
Exercise 5.1
Exercise 5.1
Q1. In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
(i) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.
(ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time.
(iii) The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre.
(iv) The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8 % per annum.
Q2. Write first four terms of the AP, when the first term a and the common difference d are given as follows:
(i) a = 10, d = 10 (ii) a = –2, d = 0
(iii) a = 4, d = – 3 (iv) a = – 1, d = 1/2
(v) a = – 1.25, d = – 0.25
Q3. 3. For the following APs, write the first term and the common difference:
(i) 3, 1, – 1, – 3, . . . (ii) – 5, – 1, 3, 7, . . .
(iv) 0.6, 1.7, 2.8, 3.9, . . .
Q4. Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
5. Arithmetic Progressions
Exercise 5.2
Exercise 5.2
Q1. Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP:
Q2. Choose the correct choice in the following and justify :
(i) 30th term of the AP: 10, 7, 4, . . . , is
(A) 97 (B) 77 (C) –77 (D) – 87
Q3. In the following APs, find the missing terms in the boxes :
Q4. Which term of the AP : 3, 8, 13, 18, . . . ,is 78?
Q5. Find the number of terms in each of the following APs :
(i) 7, 13, 19, . . . , 205
Q6. Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Q7. Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Q8. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Q9. If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Q10. The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Q11. Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Q12. Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Q13. How many three-digit numbers are divisible by 7?
Q14. How many multiples of 4 lie between 10 and 250?
Q15. For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Q16. Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Q17. Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Q18. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Q19. Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?
Q20. Ramkali saved Rs 5 in the first week of a year and then increased her weekly savings by Rs 1.75. If in the nth week, her weekly savings become Rs 20.75, find n.
5. Arithmetic Progressions
Exercise 5.3
Exercise 5.3
Q1. Find the sum of the following APs:
(i) 2, 7, 12, . . ., to 10 terms.
(ii) –37, –33, –29, . . ., to 12 terms.
(iii) 0.6, 1.7, 2.8, . . ., to 100 terms.
Q2. Find the sums given below :
(ii) 34 + 32 + 30 + . . . + 10
(iii) –5 + (–8) + (–11) + . . . + (–230)
Q3. In an AP:
(i) given a = 5, d = 3, an = 50, find n and Sn.
(ii) given a = 7, a13 = 35, find d and S13.
(iii) given a12 = 37, d = 3, find a and S12.
(iv) given a3 = 15, S10 = 125, find d and a10.
(v) given d = 5, S9 = 75, find a and a9.
(vi) given a = 2, d = 8, Sn = 90, find n and an.
(vii) given a = 8, an = 62, Sn = 210, find n and d.
(viii) given an = 4, d = 2, Sn = –14, find n and a.
(ix) given a = 3, n = 8, S = 192, find d.
(x) given l = 28, S = 144, and there are total 9 terms. Find a.
Q4. How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Q5. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Q6. The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Q7. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Q8. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Q9. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
5. Arithmetic Progressions
Exercise 5.4
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