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Question

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a. \[3 \times {4^{15}}\]

b. \[3 \times {4^{14}}\]

c. \[3 \times {4^{16}}\]

d. \[{3^{15}}\]

Answer
Verified

Here, in the given problem, we are to find the 15th term of the G.P. \[3,12,48,192,.....\]

So, we have our first term as,\[a = 3\], then the common ratio is obtained by second term divided by first term, i.e. \[\dfrac{{12}}{3}\]\[ = 4\]

As per the formula of the G.P,

\[{T_n} = a{r^{n - 1}}\]

The 15th term would be, \[a{r^{15 - 1}}\]\[ = a{r^{14}}\], where a is the first term and the common ratio r.

Now, we have, \[a = 3,r = 4\], the 15th term would be, \[3 \times {4^{14}}\].