Find the missing terms of the following geometric sequence. Assume all terms are positive. ​(​Hint: The geometric mean of the first and fifth terms is the third​ term.)

Question

2.5​, ​__ ,__​ , __, 1562.5​, . . .

Answer 1

The given geometric sequence is: 2.5, __, __, __, 1562.5, . . .

The common ratio (r) can be found by taking the square root of the ratio of the fifth term to the first term:
r = √(1562.5 / 2.5) = √625 = 25

Now we can find the missing terms by multiplying each term by the common ratio:
2.5 * 25 = 62.5
62.5 * 25 = 1562.5

Therefore, the missing terms are 62.5 and 312.5.