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.)
2.5, __ ,__ , __, 1562.5, . . .
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.