11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer In a G.P. the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number, the series becomes A.P., then the greatest number is  [Roorkee 1973]

    A) 8

    B) 4

    C) 24

    D) 16

    Correct Answer: A

    Solution :

    Let three numbers in G.P. are \[\frac{a}{r},\ a,\ ar\]. Condition I: \[\frac{a}{r}+a+ar=14\Rightarrow a\left( \frac{1}{r}+1+r \right)=14\] ?.(i) Condition II: \[\frac{a}{r}+1,\ a+1\] and \[ar-1\] will be in A.P., then \[2(a+1)=\frac{a}{r}+1+ar-1=\frac{a}{r}(1+{{r}^{2}})\] ......(ii) From (i) and (ii), we get \[a=4\] and \[r=2\]. So, required numbers are 2, 4, 8. Hence greatest number is 8.

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