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InterviewSolution
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Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.(i) 10, 10 + 26, 10 + 27(ii) a + b, (a + b) + b, (a + b) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), .....(iii) 12, 32, 52, 72, ......(iv) 12, 52, 72, 73, ....... |
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Answer» (i) 10, 10 + 26, 10 + 27 Common difference, d1 = 10 + 26 – 10 = 26 = 64 Common difference, d2 = 10 + 27 – 10 – 26 = 26 (2 – 1) = 64 Since, d1 = d2 Therefore, it’s an A.P. with common difference, d = 64 (ii) a + b, (a + b) + b, (a + b) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ..... Common difference, d1 = (a + 1) + b – a – b = 1 Common difference, d2 = (a + 1) + (b + 1) – (a + 1) – b = 1 Since, d1 = d2 Therefore, it’s an A.P. with common difference, d = 1 (iii) 12, 32, 52, 72, ...... Common difference, d1 = 32 – 12 = 8 Common difference, d2 = 52 – 32 = 25 – 9 = 16 Since, d1 ≠ d2 Therefore, it’s not an A.P. (iv) 12, 52, 72, 73, ....... Common difference, d1 = 52 – 12 = 24 Common difference, d2 = 72 – 52 = 24 Since, d1 = d2 Therefore, it’s an A.P. with common difference, d = 24 |
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