Ex 5.2 class 10
- Fill in the blanks in the following table given that a is the first term d is the common difference and an the nth term of the AP.
2. Choose the correct choice in the following and justify:
3. In the following APs, find the missing terms in boxes:
5. Find the number of terms in each of the following AP
(i) 7,13,19………,205
(ii) 18, 15 1/2, 13, …..,-47
6. Check whether -150 is a term of AP; 11, 8, 5, 2 ……
7. Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73
8. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106 find the 29th term
9. If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which terms of this AP is zero ?
10. The 17th term of an ap exceeds its 10th term by 7 find the common difference
11. Which Term of the AP: 3, 15, 27, 39,…. Will be 132 more than its 54th term?
12. Two APs have sim common difference the difference between the hundred terms is 100 what is the difference between their 1000th term
13. How many three digits number are divisible by 7
14. How many multiples of 4 lie between 10 and 250?
15. For what value of n, are the nth terms of two APs: 63, 65, 67,. . . and 3,10,17,. . . Equal?
16. Determine the AP whose third term is 16 and the 7th term exceed the 5th term by 12.
17. Find the 20th term from the last term of AP: 3, 8, 13, …..,253.
18. The sum of the 4th and the 8th term of an ap is 24 and the sum of the 6th and 10th terms is 44 .find the three terms of AP
19. Subba Rao started work in 1995 at an annual salary of rupees 5000 and received an increment of rupees 200 each year in which year did his income reach Rs 7000
20. Ramkali saved Rs 5 in the first week of a year and then increased her weekly savings by rupees 1.75 if in the 9th week her weekly savings become rupees 20.75 find n
Arithmetic Progression (AP) is a sequence of numbers in which the succeeding term after the first one is obtained by adding a fixed constant value to the preceding term. This fixed constant value is called the common difference of the AP. NCERT’s Class 10 Maths textbook’s chapter 5, Exercise 5.2, provides a comprehensive introduction to APs, their properties, and how to find the nth term, sum of n terms, and their applications in solving real-life problems.
Class 10 ex 5.2 begins with a concise explanation of AP and how to identify one. class 10 maths ch 5 ex 5.3, then proceeds to explain the properties of APs, such as the sum of the first n terms, the nth term of an AP, and the sum of an AP whose first and last terms are given. The formula for the nth term of an AP is a_n = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number. This formula simplifies the calculation of any term in an AP, given its position and the first term.
Ex 5.2 class 10 also delves into the real-life applications of APs, such as finding the number of steps required to climb a staircase or the number of tiles required to cover a floor. These problems require the use of the formula for the sum of n terms of an AP, given as S_n = (n/2)(2a + (n-1)d). This formula enables the computation of the sum of any n consecutive terms in an AP, given the first term and the common difference.
One crucial concept in APs is the notion of a series, which is the sum of a sequence of numbers, and it can either be finite or infinite. Exercise 5.2 class 10 maths presents various problems involving finite series, such as finding the sum of the first n even or odd numbers or finding the sum of a series where the first term is a, and the common difference is also a. These problerequire the formula for the sum of an AP and some algebraic manipulation.
Ex 5.2 also covers some fascinating properties of APs, such as the fact that the sum of the first n terms of an AP is equal to the sum of the last n terms of the same AP. This property is known as the property of symmetric sums and can be proven using the formula for the sum of an AP.
APs are also useful in solving problems involving time, distance, and speed. For instance, if a car is traveling at a constant speed of 60 km/h, the distance it covers in t hours can be modeled using an AP, where the first term is 0, and the common difference is 60. The nth term of this AP represents the distance covered in n hours, and the sum of the first n terms represents the total distance covered in n hours. This concept can be applied to problems involving multiple vehicles, different speeds, and distances.
In conclusion, Exercise 5.2 of the NCERT Class 10 Maths textbook provides a comprehensive introduction to arithmetic progressions, their properties, and their applications in real-life problems. 5.2 maths class 10 ,covers the formula for the nth term of an AP, the sum of the first n terms of an AP, and the sum of an AP whose first and last terms are given. class 10 maths ex 5.2 also explores some intriguing properties of APs, such as the property of symmetric sums. Ex 5.2 class 10 provides various examples and problems that allow students to apply the concepts they have learned and develop their problem-solving skills. A solid understanding of the concepts of arithmetic progressions is crucial for students to excel in mathematics and other fields that require a thorough comprehension of algebraic concept
Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 1.2
Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 2.2
Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/
MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8
Ex 5.2 class 10
Ex 5.2 class 10
Ex 5.2 class 10
Ex 5.2 class 10