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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) 3, 3, 3, 3, ....(ii) p, p+90, p+180, p+270, .... where p = (999)999(iii) 1.0, 1.7, 2.4, 3.1, ......(iv) - 225, - 425, - 625, - 825, ....... |
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Answer» (i) 3, 3, 3, 3, .... Common difference, d1= 3 – 3 = 0 Common difference, d2= 3 – 3 = 0 Since, d1 = d2 Therefore, it’s an A.P. with common difference, d = 0 (ii) p, p+90, p+180, p+270, .... where p = (999)999 Common difference, d1= p + 90 – p = 90 Common difference, d2 = p + 180 – p – 90 = 90 Since, d1 = d2 Therefore, it’s an A.P. with common difference, d = 90 (iii) 1.0, 1.7, 2.4, 3.1, ...... Common difference, d1= 1.7 – 1.0 = 0.7 Common difference, d2= 2.4 – 1.7 = 0.7 Since, d1 = d2 Therefore, it’s an A.P. with common difference, d = 0.7 (iv) - 225, - 425, - 625, - 825, ....... Common difference, d1 = - 425 + 225 = - 200 Common difference, d2 = - 625 + 425 = - 200 Since, d1 = d2 Therefore, it’s an A.P. with common difference, d = - 200 |
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