Final answer:
The common ratio of the geometric sequence with the third term being 6 and the fifth term being 150 is found to be 5.
Step-by-step explanation:
The student is asking to find the common ratio of a geometric sequence with positive terms, where the third term is 6 and the fifth term is 150. To solve this, we can use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and r is the common ratio.
Since we know the third and fifth terms, we can create the following equations:
- a3 = a1 × r2 = 6
- a5 = a1 × r4 = 150
Dividing the second equation by the first equation gives us r2 = 150/6 = 25. Therefore, the common ratio r is the square root of 25, which is 5.