Questions
The sum of three numbers in G.P. is 14. If one is added to the first and second numbers and I is subtracted from the third, the new numbers are in A.P. The smallest of them is
detailed solution
Correct option is A
Let the numbers be a, ar, ar2. Then,a + ar + ar2 = 14 (given)----------(1)Now,a + 1 ar + l, ar2- 1 are in A.p.⇒2(ar+1)=a+1+ar2−1⇒2ar+2=a+ar2----2From (1) and (2),2ar+2=14-aror 3ar= 12or ar=4 --------(3)From (1),a+4+4r=L4 a+4r=10 --------(4)From (3) and (4),a+16a=10⇒a=2,8Hence, the smallest number is 2.Similar Questions
If the roots of the equation,
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