Question : The average (arithmetic mean) of $3^{30},3^{60},$ and $3^{90}$ is:
Option 1: $3^{27}+3^{57}+3^{87}$
Option 2: $3^{60}$
Option 3: $3^{29}+3^{59}+3^{89}$
Option 4: $3^{177}$
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Correct Answer: $3^{29}+3^{59}+3^{89}$
Solution :
Given: The numbers are $3^{30},3^{60},$ and $3^{90}$
Arithmetic mean
$=\frac{3^{30}+3^{60}+3^{90}}{3}$
$=\frac{3(3^{29}+3^{59}+3^{89})}{3}$
$=3^{29}+3^{59}+3^{89}$
Hence, the correct answer is $3^{29}+3^{59}+3^{89}$.
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