Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsGeometric progression2 Marks
Question
Which term of the $G.P. 4,12, 36, ...$ is $324 ?$
✓
Answer
The $G.P.$ is $4,12,36, \ldots$.
$\therefore a =4, r =\frac{12}{4}=3, T_{ n }=324, n =?$
$T_{ n }= a \cdot r ^{ n -1}$
$\therefore 324=4 \cdot(3)^{ n -1}$
$\therefore \frac{324}{4}=(3)^{ n -1}$
$\therefore 81=(3)^{ n -1}$
$\therefore(3)^4=(3)^{ n -1}$
$\therefore 4= n -1(\because$ Base are equal, then Index are equal)
$\therefore n =5$
Hence, the fifth term of the $G.P.$ is $324.$
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