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The sum of three positive numbers constitutingarithmetic progressioni no 4, tothose numbers respectively. We get a geometricprogression, then the numbers are- |
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Answer» Let a-d,a , a+d are in AP ACCORDING to sum a-d+a+a+d=153a=15a=5the terms will be 5-d,5,5+dwhen 1,4,19 are added to the terms they are in GP5-d+1,5+4,5+d+19 are in GPcommon ratio must be equalthe terms are 6-d,9,24+d9/(6-d)=(24+d)/9cross multiplying we get(6-d)(24+d)=9*9 (6*24+6d-24d-d^2)=81 (144-18d-d^2)=81 d^2+18d=144+81 =225 d^2+18d-225=0 by solving this we get d=8,-26 the numbers may be -3,5,3 or 31,5,-21 given that the sum is 15 so the numbers may not be -3,5,3 so the numbers are 31,5,-21 |
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