Ex 5.1, 4 (vi) - (x) - Chapter 5 Class 10 Arithmetic Progressions

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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. (vi) 0.2, 0.22, 0.222, 0.2222 …. 0.2, 0.22, 0.222, 0.2222 Difference between second and first term = 0.22 – 0.2 = 0.22 – 0.20 = 0.02 Difference between third and second term = 0.222 – 0.22 = 0.222 – 0.220 = 0.002 Since difference is not same 0.02 ≠ 0.002 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. (vii) 0, − 4, − 8, − 12 … 0, –4, –8, –12 Difference between second and first term = ( – 4) – 0 = –4 Difference between third and second term = –8 – (– 4) = –8 + 4 = –4 Difference between fourth and third term = –12 – (–8) = –12 + 8 = –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 = 4th term + common difference = – 12 + (–4) = – 12 – 4 = –16 6th term = 5th term + common difference = – 16 + (–4) = –20 7th term = 6th term + common difference = –20 + (–4) = –24 Hence, 5th 6th and 7th term are –16, –20, –24 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. (viii) (−1)/2 , (−1)/2 , (−1)/2 , (−1)/2 … (−1)/2 , (−1)/2 , (−1)/2 , (−1)/2 … All terms are same Difference between second and first term = ((− 1)/2) −" " ((− 1)/2) = (−1)/2 + 1/2 = 0 Similarly difference between third and second term = ((− 1)/2) −" " ((− 1)/2) = (−1)/2 + 1/2 = 0 Difference between fourth and third term = ((− 1)/2) −" " ((− 1)/2) = (−1)/2 + 1/2 = 0 Since difference is same, it is an AP Common difference = d = 0 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 = (−1)/2 + 0 = (−𝟏)/𝟐 6th term = 5th Term + Common difference = (−1)/2 + 0 = (−𝟏)/𝟐 7th term = 6th Term + Common difference = (−1)/2 + 0 = (−𝟏)/𝟐 Therefore, 5th , 6th and 7th terms are (−𝟏)/𝟐 , (−𝟏)/𝟐 , (−𝟏)/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. (ix) 1, 3, 9, 27 … 1, 3, 9, 27 Difference between second and first term = 3 – 1 = 2 Difference between third and second term = 9 – 3 = 6 Since, difference is not same 2 ≠ 6 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. (x) a, 2a, 3a, 4a … a, 2a, 3a, 4a Difference between second and first term = 2a – a = a Difference between third and second term = 3a – 2a = a Difference between fourth and third term = 4a – 3a = a Since difference is same, it is an AP Common difference = d = a 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 = 4a + a = 5a 6th term = fifth term + common difference = 5a + a = 6a Seventh term = sixth term + common difference = 6a + a = 7a Hence, 5th, 6th and 7th terms are 5a , 6a, 7a