A) (1, 5, 25)
B) (6, 32, 128)
C) (4, 10, 17)
D) (2, 8, 21)
Correct Answer: A
Solution :
(a): Let ?a? be the first term of the GP and ?r? be the common ratio. Then the three terms which are in GP can be written as\[\frac{a}{r}a,ar\]. According to question, \[\frac{a}{r}\times a\times ar=125\] \[\Rightarrow \]\[{{a}^{3}}=125\] \[\Rightarrow \]\[a=5\] Also, \[\frac{a}{r}+a+ar=31\] \[\Rightarrow \]\[\frac{5}{r}+5+5r=31\] \[\Rightarrow \]\[5{{r}^{2}}-26r+5=0\] \[\Rightarrow \]\[(5r-1)(r-5)=0\] \[\Rightarrow \] \[r=\frac{1}{5},5\]
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