# class 10 maths chapter 5

Did you find NCERT Solutions Class 10 Maths chapter 5 Arithmetic Progressions helpful? Clearly, adjacent terms of this series do not have the same difference (vii) $$0,-4,-8,-12, \dots$$ Click Here Show that a1, a2 … , an , … form an AP where an is defined as below. Therefore, using nth term formula, we get. Common difference, d = Second term — First term We know that , NCERT Solutions Chapter 5 Arithmetic Progressions Class 10 Maths is given here which will be useful in completing homework on time and improving your problem solving skills. (xii) √2, √8, √18, √32 … (iv) 1/15, 1/12, 1/10, …… , to 11 terms, And common difference, d = a2 − a1 = 7−2 = 5. Therefore, this given A.P. Thus, we can conclude now, that the rungs are decreasing in an order of AP. (iii) − 5 + (− 8) + (− 11) + ………… + (− 230). First term, a = S1 = 4(1) − (1)2 = 4−1 = 3, Sum of first two terms = S2= 4(2)−(2)2 = 8−4 = 4. . Clearly the series will be 3. If they form an A.P. Your email address will not be published. Let the series be $$a_{1}, a_{2}, a_{3}, a_{4} \dots$$ The second term is 1. (vi) 0.2, 0.22, 0.222, 0.2222 …. (iv) Given a3 = 15, S10 = 125, find d and a10. between them. Find the sum of the odd numbers between 0 and 50. Therefore, d = 24 and the given series forms a A.P. Therefore, and the given series doesn’t form a A.P. Hence, the total volume of concrete required to build the terrace is 750 m3. Therefore, this is not an A.P. (ii) The amount of air present in a cylinder when a vacuum pump removes $$\frac{1}{4}$$ of the air remaining in the cylinder at a time. Hence, the value of x is 35. Check whether -150 is a term of the A.P. We know, nth term of this A.P. Here, first term $$a=\frac{1}{3}$$ $$\begin{array}{l}{a_{n}=a+(n-1) d} \\ {-5=a+(18-1)(-3)} \\ {-5=a+(17)(-3)} \\ {-5=a-51} \\ {a=51-5=46}\end{array}$$ $$\begin{array}{l}{a_{n}=a+(n-1) d} \\ {-5=a+(18-1)(-3)} \\ {-5=a+(17)(-3)} \\ {-5=a-51} \\ {a=51-5=46}\end{array}$$ Cost of digging for first 2 metres = 150 + 50 = 200 and their application in solving daily life problems. Solving these NCERT Solutions will help you understand the topic completely and help you lay a greater foundation for future studies. Cost of digging for first 4 metres = 250 + 50 = 300 Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. Subtracting equation (i) from equation (ii), 10. We know that 9, 17, 25 …. (iii) $$\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3} \ldots$$ The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. ., is its first negative term? $$\begin{array}{l}{a_{1}=a=-2} \\ {a_{2}=a_{1}+d=-2+0=-2} \\ {a_{3}=a_{2}+d=-2+0=-2} \\ {a_{4}=a_{3}+d=-2+0=-2}\end{array}$$ having first term as 105 and common difference as 7. 3, 8, 13, …, 253. Clearly, we can see here, the adjacent terms of this series do not have the common difference between them. [Hint :Sx – 1 = S49 – Sx ]. Similarly, the 25th term could be written as; It can be seen, the number of logs in 16th row is 5 as the numbers cannot be negative. It is given that, 7th term exceeds the 5th term by 12. First four terms of this AP. Cost of digging for first 3 metres = 200 + 50 = 250 We know that If in the nth week, her weekly savings become Rs 20.75, find n. Given that, Ramkali saved Rs.5 in first week and then started saving each week by Rs.1.75. The houses of a row are numbered consecutively from 1 to 49. be 78. Taxi fare for $$1^{st}$$ km = 15 (II) Given that contains 38 terms and the sum of the terms of this A.P. Clearly, the terms of this series do not have the common difference between them. Therefore, 200 logs can be placed in 16 rows and the number of logs in the 16th row is 5. This chapter has Arithmetic Progression Derivation of the nth term and sum of the first n terms of an A.P. (ii), we get. Given, nth term of these A.P.s are equal to each other. [Hint: Find n for an < 0]. The examples mentioned in the chapter will help you while solving the exercise problems. Which of the following are APs? 6. because every term is 50 more than the preceding term. 11. And First four terms of this A.P. Again putting the eq. (iv) $$a=-1, d=\frac{1}{2}$$ NCERT Solutions Maths Class 10 Chapter 5 Arithmetic Progressions are provided by Vedantu. 5.7). (ii) Given a = 7, a13 = 35, find d and S13. will be 10, 20, 30, and 40. If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is S1)? 16. Therefore, 999-5 = 994 is the maximum possible three-digit number that is divisible by 7. Therefore, 128 three-digit numbers are divisible by 7. (i) 2, 4, 8, 16 … We can see here, that this series forms an A.P. 13. (II) Given that Their number of years of working experience and knowledge might help students in solving the questions of chapter 5 Maths Class 10 solutions. Common difference, d = second term - First term (iii) 1/3, 5/3, 9/3, 13/3 …. We shall also see how to find their nth terms and the sum of n consecutive terms, and use this knowledge in solving some daily life problems. Ans : (i) It can be observe that 17. Putting the value of a from equation (v), we get. Required fields are marked *. $$\begin{array}{l}{=7+(8-1) 3} \\ {=7+(7) 3} \\ {=7+21=28}\end{array}$$ will be $$-1,-\frac{1}{2}, 0 \text { and } \frac{1}{2}$$ $$\begin{array}{l}{a_{1}=a=10} \\ {a_{2}=a_{1}+d=10+10=20} \\ {a_{3}=a_{2}+d=20+10=30} \\ {a_{4}=a_{3}+d=30+10=40} \\ {a_{5}=a_{4}+d=40+10=50}\end{array}$$ Let −230 be the nth term of this A.P., and by the nth term formula we know. Therefore, the contractor has to pay Rs 27750 as penalty. We have to find the term of this A.P. In each stroke, the vacuum pump removes 1/4th of air remaining in the cylinder at a time. It will help you stay updated with relevant study material to help you top your class! (ii) $$-5,-1,3,7 \ldots$$ 7. Here, the terms and their difference are; Since, an+1 – an or the common difference is same every time. 18. In a school, students thought of planting trees in and around the school to reduce air pollution. If they form an AP, find the common difference d and write three more terms. Hence a=46 $$10000\left(1+\frac{8}{100}\right), 10000\left(1+\frac{8}{100}\right)^{2}, 10000\left(1+\frac{8}{100}\right)^{3}, 10000\left(1+\frac{8}{100}\right)^{4}$$ And the length of the wood required for the rungs will be equal to the sum of the terms of AP series formed. (iv) We know that if Rs P is deposited at r% compound interest per annum for n years, our money will be $$\mathbf{P}\left(1+\frac{r}{100}\right)^{n}$$ after n years. (xiv) $$\mathrm{1}^{2}, 3^{2}, 5^{2}, 7^{2}, \ldots$$ What is the second term? The concepts are explained with different types of problems solving techniques and finding the nth term of an AP. In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? We can see that the cost of these prizes are in the form of A.P., having common difference as −20 and first term as P. Therefore, the value of each of the prizes was Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40. consists of 50 terms of which 3rd term is 12 and the last term is 106. Let the series be $$a_{1}, a_{2}, a_{3}, a_{4} \dots$$ Therefore, this is not an A.P. This chapter comes under unit 3 algebra and this unit has 20 marks allotted in the examination. Two APs have the same common difference. will be 10, 20, 30, and 40. Since, an+1 – an or common difference is same every time. Therefore, the A.P. NCERT Solutions for class 10 Maths Chapter 5 Exercise 5.2 AP ( Samantar Shreni ) in Hindi Medium and English Medium free to download in PDF Format updated for current academic year 2020-2021. All these are divisible by 4 and thus, all these are terms of an A.P. How many multiples of 4 lie between 10 and 250? Here, first term, a = —5 (iv) a = – 1, d = 1/2 ., To find the first negative term of the series, an < 0. Therefore, we can see that these odd numbers are in the form of A.P. Here, first term , a=0.6 There are ten potatoes in the line. (viii) Given an = 4, d = 2, Sn = − 14, find n and a. Chapter 5 - Set & Functions. Here, first term , a=0.6 Cost of digging for first 3 metres = 200 + 50 = 250 (iv) The amount of money in the account every year, when ₹ 10000 is deposited at compound interest at 8 % per annum. has 27 terms in it. Therefore, 65th term was 132 more than 54th term. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees and so on till class XII. We will keep adding updated notes, … You can also check out NCERT Solutions of other classes here. For an A.P $$a_{n}=a+(n-1) d$$ (ix) Given a = 3, n = 8, S = 192, find d.