For more information on the study resources we provide, register with BYJU’S website or download BYJU’S Learning App for a customised learning experience. because every term is 50 more than the preceding term. Now as we know. will be 10, 20, 30, and 40. Let the series \( a_{1,} a_{2}, a_{3}, a_{4} \dots \) Find the sum of first 40 positive integers divisible by 6. [Hint: Find n for an < 0]. We know, nth term of this A.P. For a better understanding of this chapter, you should also see summary of Chapter 5 Arithmetic Progressions , Maths, Class 10. Clearly 15, 23, 31, 39.… forms an A.P. ., Thus, first term, a = 121 Common difference, d = 117-121= -4 By the nth term formula, Frequently Asked Questions on Chapter 5 – Arithmetic Progressions. Show that a1, a2 … , an , … form an AP where an is defined as below. having first term as 200 and common difference as 50. If they form an A.P. Now, by putting both the values of d, we get, a = 3 – 4d = 3 – 4(1/2) = 3 – 2 = 1, when d = 1/2, a = 3 – 4d = 3 – 4(-1/2) = 3+2 = 5, when d = -1/2, S16 = 16/2 [2 +(16-1)1/2] = 8(2+15/2) = 76, S16 = 16/2 [2.5+(16-1)(-1/2)] = 8(5/2)=20. First three-digit number that is divisible by 7 are; All are three digit numbers are divisible by 7 and thus, all these are terms of an A.P. Clearly, it can be observed that the adjacent terms of this series do Download NCERT Solutions For Class 10 Maths Chapter 5 Arithmetic Progressions PDF. We know that having first term as 105 and common difference as 7. On subtracting equation (i) from (ii), we get, From equation (i), putting the value of d,we get. The distances of potatoes from the bucket are 5, 8, 11, 14…, which is in the form of AP. Therefore, d = -4 and the given series forms a A.P. (xiv) 12, 32, 52, 72 … If 17th term of an A.P. 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. Exercise 5.1– 4 questions 1 MCQ and 3 descriptive type questionsExercise 5.2– 20 questions, 1 fill in the blanks, 2 MCQ’s, 7 Short answer questions and 10 Long answer questionsExercise 5.3– 20 Questions 3 fill in the blanks, 4 daily life examples, and 13 descriptive type questionsExercise 5.4 5 Questions- 5 Long answer questions. 5.1 Introduction In this chapter, we shall discuss patterns which we come across in our day-to-day life in which succeeding terms are obtained by adding a fixed number to the preceding terms. Did you find NCERT Solutions Class 10 Maths chapter 5 Arithmetic Progressions helpful? Find the common difference. Therefore , the series will be 10,20,30,40,50.. Therefore, the given series doesn’t form a A.P. Solving these NCERT Solutions will help you understand the topic completely and help you lay a greater foundation for future studies. Therefore, number of trees planted by 1 section of the classes = 78, Number of trees planted by 3 sections of the classes = 3×78 = 234. (ii) \( 2, \frac{5}{2}, 3, \frac{7}{2}, \ldots \) Given the AP series is 121, 117, 113, . The second term is 1. because every term is 8 more than the preceding term ., is its first negative term? \( -1,-\frac{1}{2}, 0, \frac{1}{2} \) \( d=-3, n=18, a_{n}=-5 \) NCERT Solutions for each subject and class are available for students to download. Clearly, it can be observed that the adjacent terms of this series do We know that , Hence, ak + 1 − ak is same every time. exceeds its 10th term by 7. (ii), we get. In each stroke, the vacuum pump removes \(\frac{1}{4}\) of air remaining in the cylinder at a time. (iv) -10, – 6, – 2, 2 … Since, an+1 – an or the common difference is same every time. Here, the terms and their difference are; Since, an+1 – an or the common difference is same every time. 5.5 Summary 12. Here, first term, a = 3 Hence, the value of x is 35. Therefore, d = a and the given series forms a A.P. Also please like, and share it with your friends! (ii) 2, 5/2, 3, 7/2 …. It can be observed that the number of trees planted by the students is in an AP. \( =(-1)-(-5)=-1+5=4 \) Therefore, the competitor will run a total distance of 370 m. 1. 3, 8, 13, 18, … is 78? 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. 3, 8, 13, …, 253. Let there be n terms in the A.P., thus the formula for last term can be written as; Thus, this A.P. Otherwise you can also buy it easily online. (i) 2, 7, 12 ,…., to 10 terms. Find the sum of the odd numbers between 0 and 50. a4 – a3 = √12 – √9 = 2√3 – √3×√3 = √3(2-√3). NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression is presented here for the benefit of the students preparing for the board examination. \) Let there be n terms of the AP. Clearly, n is not an integer but a fraction. Thus we can understand that the width of step by ½ m each time when height is ¼ m. And also, given length of the steps is 50m all the time. is 9, 17, 25 … must be taken to give a sum of 636? Find the number of terms in each of the following A.P. The sum of 4th and 8th terms of an A.P. Four terms of this A.P. (ix) Given a = 3, n = 8, S = 192, find d. What is the total distance the competitor has to run? Therefore, we can write the given AP in reverse order as; and common difference, d = 248 − 253 = −5. (x) Given l = 28, S = 144 and there are total 9 terms. Clearly, 150, 200, 250, 300 forms an A.P. 14. Therefore, using nth term formula, we get. First four terms of this AP. A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. 20. 6. (ii) \(-5,-1,3,7 \ldots \) \( \begin{array}{l}{=7+(8-1) 3} \\ {=7+(7) 3} \\ {=7+21=28}\end{array}\) (ii) \( a=-2, d=0 \) Here, first term, a = —5 Therefore, in 11th year, his salary will be Rs 7000. Therefore, we can see that these odd numbers are in the form of A.P. will be – 2, – 2, – 2 and – 2. Cost of digging for first 3 metres = 200 + 50 = 250 = 1-3=-2 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 A.P. Therefore the series will be \( -2,-2,-2,-2 \ldots\) Therefore, the A.P. (v) \( a=-1.25, d=-0.25\) Which term of the A.P. Therefore, 20th term from the last term of the AP 3, 8, 13, …, 253.is 158. will be 100. By going through the summary part you can cover the entire chapter in a few points which help in memorizing the essential concepts. Here, first term , a=0.6 (xii) \( \sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \dots \) (iii) \( -1.2,-3.2,-5.2,-7.2, \dots \) Therefore, volumes will be \(V\left(\frac{3 V}{4}\right) \cdot\left(\frac{3}{4} V\right)^{2} \cdot\left(\frac{3}{4} V\right)^{3} \dots\) Therefore, 234 trees will be planted by the students. Hence common difference , d=2 because every next term is 8 more than the preceding term. Let a total of 200 logs be placed in n rows. Clearly the series will be \( 1.25,-1.50,-1.75,-2.00 \ldots \ldots . Therefore, after every year, our money will be Therefore, volumes will be \(V\left(\frac{3 V}{4}\right) \cdot\left(\frac{3}{4} V\right)^{2} \cdot\left(\frac{3}{4} V\right)^{3} \dots\) (ix) \( 1,3,9,27, \dots \) 15. (vii) 0, – 4, – 8, – 12 … Will be \( -2,-2,-2 \text { and }-2 \) So, the width of steps forms a series AP in such a way that; Volume of concrete required to build the first step = ¼ ×1/2 ×50 = 25/4, Volume of concrete required to build the second step =¼ ×1/×50 = 25/2, Volume of concrete required to build the second step = ¼ ×3/2 ×50 = 75/2. P is deposited at r% compound interest per annum for n years, the amount of money will be: Therefore, after each year, the amount of money will be; 10000(1+8/100), 10000(1+8/100)2, 10000(1+8/100)3……. Move Class 10 Maths Chapter 5 main page for … Overview Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5 Miscellaneous Exercise. 14. \( \begin{array}{l}{a_{1}=a=-2} \\ {a_{2}=a_{1}+d=-2+0=-2} \\ {a_{3}=a_{2}+d=-2+0=-2} \\ {a_{4}=a_{3}+d=-2+0=-2}\end{array} \) \) Let the series \(a_{1}, a_{2}, a_{3}, a_{4}, a_{5} \ldots \) Find this value of x. Now, we can see the volumes of concrete required to build the steps, are in AP series; Common difference, d = 25/2 – 25/4 = 25/4, Sn = n/2[2a+(n-1)d] = 15/2(2×(25/4 )+(15/2 -1)25/4). (viii) Given an = 4, d = 2, Sn = − 14, find n and a. (iii) and (iv), in eq. Common difference, d = second term - First term A ladder has rungs 25 cm apart. (iv) Given a3 = 15, S10 = 125, find d and a10. 10. \(10000\left(1+\frac{8}{100}\right), 10000\left(1+\frac{8}{100}\right)^{2}, 10000\left(1+\frac{8}{100}\right)^{3}, 10000\left(1+\frac{8}{100}\right)^{4}\)

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