Am I doing this correctly

Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 75 and the 8th term is 48.

A) 60***
B) 66
C) 57
D) 51.5
E) 59
F) 68

r^2 = 48/75 = 16/25
r = 4/5 7th term = 75 * 4/5 = 60

The geometric mean is the nth root of the product of n numbers.

a7 = √ ( 75 * 48 )

a7 = √3600 = 60

Thanks for the help and showing me an easier way to do it.

You're welcome.

Yes, you are doing it correctly. To find the 7th term in a geometric sequence, you can use the formula:

nth term = a * r^(n-1)

Where:
- "a" is the first term of the sequence
- "r" is the common ratio
- "n" is the position of the term you want to find

In this case, you are given the 6th term as 75 and the 8th term as 48. So, you can use the given information to find the common ratio "r".

To find "r", you can divide the 8th term by the 6th term:

r^2 = 48/75 = 16/25

Take the square root of both sides to get:

r = √(16/25) = 4/5

Now that you have the common ratio "r", you can use it to find the 7th term by plugging it into the formula:

7th term = 75 * (4/5)^6

Simplifying:

7th term = 75 * (2^2 / 5^2)^3 = 75 * (4/25)^3 = 75 * 64/125 = 300/5 = 60

Therefore, the 7th term in the geometric sequence is 60. So the correct answer is A) 60.