question_answer

If \[l,m,n\] are the\[{{p}^{th}},{{q}^{th}}\]and \[{{r}^{th}}\]term of a G.P. If all terms are positive, then is equal to

A)  0                   

B)  1              

C)  2                                

D)  3

Correct Answer: A

Solution :

[a] Let a and x be the 1st term and common ratio of the G.P respectively. \[l=a{{x}^{p-1}}\Rightarrow \log a=loga+(p-1)logx\] \[m=a.{{x}^{q-1}}\Rightarrow logm=loga+\left( q-1 \right)logx\] \[n=a.{{x}^{r-1}}\Rightarrow \log n=\log a+(r-1)\log x\] \[=0+logx\times 0=0\] Hence, option [a] is correct.