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The terms `a_1, a_2, a_3`from an arithmetic sequence whose sum s 18. The terms `a_1+1,a_2, a_3,+2,`in that order, form a geometric sequence. Then the absolute value ofthe sum of all possible common difference of the A.P. is ________. |
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Answer» Correct Answer - (-1) Let `a_(1)=a-d,a_(2)=a,a_(3)=a+d` `therefore3a=18` or a=6 Hence, the number in A.P. `6-d,d,6+d` `a_(1)+1,a_(2),a_(3)+2` in G.P. i.e., 7-d,6,8+d in G.P. `therefore` 36=(7-d)(8+d) `36=56-d-d^(2)` `d^(2)+d-20=0` Hence, the sum of all possible common different is -1. |
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