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​, . . .
a2= ? a3=? a4=?

Answer 1

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