Insert five geometric means between 1/8 and 8.
1/8 __ __ __ __ __ 8 or 1/8 __ __ __ __ __ 8
To find the five geometric means between 1/8 and 8, first we need to find the common ratio (r). The common ratio is found by taking the nth root of the final term divided by the first term, where n is the number of terms. In this case, the first term is 1/8 and the final term is 8.
r = (8)^(1/7) / (1/8)^(1/7)
Now we can calculate the common ratio:
r = 2 / (1/2)
r = 2 * 2
r = 4
Now that we have the common ratio (r = 4), we can find the geometric means by successively multiplying the previous term by the common ratio:
1/8 * 4 = 1/2
1/2 * 4 = 2
2 * 4 = 8
8 * 4 = 32
32 * 4 = 128
128 * 4 = 512
Therefore, the five geometric means between 1/8 and 8 are:
1/8, 1/2, 2, 8, 32, 128, 512.
6 terms later, so
r^6 = 8/(1/8) = 64
r = ±2
so fill in the terms