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, . . .
a2= ? a3=? a4=?
The common ratio can be found by taking the square root of the fifth term divided by the first term:
Common ratio (r) = sqrt(1562.5/2.5) = sqrt(625) = 25
Now, we can find the missing terms by multiplying the common ratio by the previous term:
a2 = 2.5 * 25 = 62.5
a3 = 62.5 * 25 = 1562.5 (which is already given)
a4 = 1562.5 * 25 = 39062.5
Therefore, the missing terms are:
a2 = 62.5
a3 = 1562.5
a4 = 39062.5