# Ex 5.1, 4 (xi) - (xv) - Chapter 5 Class 10 Arithmetic Progressions

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 5.1 ,4 Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xi) a, a2, a3, a4 a, a2 , a3 , a4 Difference between second and first term = a2 a = a (a 1) Difference between third and second term = a3 a2 = a2 (a 1) Since, difference is not same. a (a 1) a2 (a 1) Hence it is not an AP Ex 5.1 ,4 Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xii) 2, 8, 18, 32 2 , 8 , 18 , 32 Difference between second and first term = 8 2 = (2 2 2) 2 = (2 22) 2 = 2 2 2 = 2 Difference between third and second term = 18 8 = (3 3 2) (2 2 2) = (32 2) (22 2) = 3 2 2 2 = 2 Difference between fourth and third term = 32 18 = (4 4 2) (2 3 3) = (42 2) (32 2) = 4 2 3 2 = 2 Since difference is same, it is an AP Common difference = d = 2 We have to find next 3 terms, We are given 4 terms So, we need to find 5th, 6th and 7th term Fifth term = fourth term + common difference = 32 + 2 = (4 4 2) + 2 = (42 2) + 2 = 4 2 + 2 = 5 2 Sixth term = Fifth term + Common difference = 5 2 + 2 = 6 2 Seventh term = Sixth term + common difference = 6 2 + 2 = 7 2 Hence, 5th, 6th and 7th terms are 5 2 , 6 2, 7 2 Ex 5.1 ,4 Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiii) 3, 6, 9, 12 3 , 6 , 9 , 12 Difference between second and first term = 6 3 = (3 2) 3 = 3 2 3 = 3 2 3 1 = 3 ( 2 1) Difference between third and second term = 9 6 = (3 3) (3 2) = 3 3 3 2 = 3 ( 3 2) The difference is not common So, it is not A.P. Ex 5.1 ,4 Which of the following are APs? If they form an A.P. find the common difference d and write three more terms (xiv) 12, 32, 52, 72 12, 32, 52, 72 Difference between second and first term = 32 12 = 9 1 = 8 Difference between third and second term = 52 32 = 25 9 = 16 Difference is not same So, it is not A.P Ex 5.1 ,4 Which of the following are APs? If they form an A.P. find the common difference d and write three more terms (xv) 12, 52, 72, 73 12, 52, 72, 73 Difference between second and first term = 52 12 = 25 1 = 24 Difference between third and second term = 72 52 = 49 25 = 24 Difference between fourth and third term = 73 49 = 24 Since difference is same, it is an AP. Common difference = d = 24 We have to find next 3 terms, We are given 4 terms So, we need to find 5th, 6th and 7th term Fifth term = fourth term + common difference = 73 + 24 = 97 Sixth term = fifth term + common difference = 97 + 24 = 121 Seventh term = sixth term + common difference = 121 + 24 = 145 So, next 3 terms of AP are 97, 121 and 145

Checking if AP or not and finding a, d

Chapter 5 Class 10 Arithmetic Progressions

Concept wise

- Checking if AP or not and finding a, d
- Finding nth term
- Finding n
- Finding AP
- Finding nth term from end
- Divisible/ multiples
- Statement questions - nth term
- Finding sum of n terms
- Finding number of terms given s
- Given nth term finding s
- Statement questions - Sum of n terms
- Determining AP and finding sum

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.