If the 5 th term of a geometric sequence is 1875 and the $7^{\text {th }}$ term is 46875 . Find the first three terms of the sequence.
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Answer

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Answer

Therefore, the first three terms of the sequence are $\boxed{3, 15, 75}$.

Steps

Step 1 ：Given that the common ratio is $r$, we have $r^2 = \frac{46875}{1875} = 25 = 5^2$. Therefore, $r = 5$.

Step 2 ：The 1st term is $\frac{1875}{r^4} = \frac{1875}{625} = 3$.

Step 3 ：So, the first three terms are $3, 3 \times 5 = 15, 15 \times 5 = 75$.

Step 4 ：Therefore, the first three terms of the sequence are $\boxed{3, 15, 75}$.