If the 5 th term of a geometric sequence is 1875 and the $7^{th}$ 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 $3, 15, 75$ .

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 $3, 15, 75$ .