Question

one of the 5 geometric means between 1/3 and 243 is

Answer 1

Let the geometric means be a1, a2, a3, a4 and a5
Then, 1/3, a1, a2, a3, a4, a5, 243 form GP
Here 1/3 is the 1st term and 243 is the 7th term
Let r be the common ratio
$\frac{1}{3} \times {r}^{7 - 1} = 243 \\ {r}^{6} = 243 \times 3 = {3}^{6} \\ so \: \: r = 3 \\ \\ therefore \\ a1 = \frac{1}{3} \times 3 = 1 \\ a2 = a1 \times 3 = 3 \\ a3 = a2 \times 3 = 9 \\ a4 = a3 \times 3 = 27 \\ a5 = a4 \times 3 = 81$

Answer 2

Step-by-step explanation:

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