# Ex 5.1, 4 (i) - (v) - Class 10

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 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. (i) 2, 4, 8, 16 … 2, 4, 8, 16….. Difference of second and first term = 4 – 2 = 2 Difference of third and second term = 8 – 4 = 4 Since 2 ≠ 4 Difference is not same 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. (ii) 2, 5/2, 3, 7/2….. 2, 5/2 , 3 , 7/2 , ….. Difference between second and first term = 5/2 – 2 = (5 − 2 × 2)/2 = (5 − 4)/2 = 1/2 Difference between third and second term = 3 – 5/2 = (3 × 2 − 5)/2 = (3 × 2 − 5)/2 = (6 − 5)/2 = 1/2 Difference between fourth and third term = 7/2 – 3 = (7− 3 × 2)/2 = (7 − 6)/2 = 1/2 Since difference is same, it is an AP Common difference = d = 1/2 We have to find next three terms We are given 4 terms . So, we have to find 5th , 6th & 7th terms . 5th term = 4th term + common difference = 7/2 + 1/2 = (7 + 1)/2 = 8/2 = 4 6th term = 5th term + common difference = 4 + 1/2 = (4 × 2 + 1)/2 = 9/2 7th term = 6th term + common difference = 9/2 + 1/2 = (9 + 1)/2 = 10/2 = 5 Hence 5th , 6th and 7th terms are 4, 9/2 , 5 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. (iii) − 1.2, − 3.2, − 5.2, − 7.2 … – 1.2, – 3.2, – 5.2, – 7.2 Difference between second and first term = – 3.2 – (–1.2) = – 3.2 + 1.2 = – 2.0 = – 2 Difference between third and second term = – 5.2 – ( – 3.2) = – 5.2 + 3.2 = – 2.0 = – 2 Difference between fourth and third term = – 7.2 – – 5.2 = – 7.2 + 5.2 = – 2.0 = – 2 Since difference is same, it is an AP Common difference = d = –2 We have to find next three terms We are given 4 terms . So, we have to find 5th , 6th & 7th terms . 5th term = fourth term + common difference = – 7.2 + – 2 = – 7.2 – 2 = – 9.2 6th term = fifth term + common difference = – 9.2 + – 2 = – 9.2 – 2 = – 11.2 7th term = sixth term + common difference = – 11.2 + – 2 = – 11.2 – 2 = – 13.2 Hence 5th , 6th and 7th terms are – 9.2, – 11.2, – 13.2 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. (iv) − 10, − 6, − 2, 2 … – 10, – 6, – 2, 2, …. Difference between 2nd and 1st term = – 6 – ( – 10) = – 6 + 10 = 4 Difference between third and second term = – 2 – ( – 6) = – 2 + 6 = 4 Difference between fourth and third term = 2 – (– 2) = 2 + 2 = 4 Since difference is same, it is an AP Common difference = d = 4 We have to find next three terms We are given 4 terms . So, we have to find 5th , 6th & 7th terms . 5th term = fourth term + common difference = 2 + 4 = 6 6th term = fifth term + common difference = 6 + 4 = 10 7th term = sixth term + common difference = 10 + 4 = 14 Hence 5th , 6th and 7th terms are 6, 10 , 14 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. (v) 3,3 + √2, 3 + 2 √2,3 + 3 √2…….. 3, 3 + √2 , 3 + 2√2 , 3 + 3√2 , ……. Difference between second and first term = 3 + √2 – 3 = √2 Difference between third and second term = (3 + 2√2 ) – (3 + √2 ) = 3 + 2√2 – 3 – √2 = 3 – 3 + 2√2 – √2 = 0 + √2 (2 – 1) = √2 (1) = √2 Difference between fourth and third term = (3 + 3√2 ) – (3 + 2√2) = 3 + 3√2 – 3 – 2√2 = 3 – 3 + 3√2 – 2√2 = 0 + 3√2 – 2√2 = √2 (3 – 2 ) = √2 × 1 = √2 Since difference is same, it is an AP Common difference = d = √2 We have to find next three terms We are given 4 terms . So, we have to find 5th , 6th & 7th terms . 5th term = fourth term + common difference = (3 + 3√2) + √2 = 3 + √2 [ 3 + 1] = 3 + √2 (4) = 3 + 4 √2 6th term = 5th term + common difference = (3 + 4√2) + √2 = 3 + √2 (4 + 1) = 3 + √2 × 5 = 3 + 5 √2 Similarly ,7th term = 6th term + common difference = (3 + 5 √2) + √2 = 3 + √2 (5 + 1) = 3 + √2 × 6 = 3 + 6 √2

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.