To solve this problem, we need to use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

First, we need to find the common ratio (r). Since we know the first term (a_1 = 3) and the last term (a_5 = 48, because we have inserted 3 geometric means between 3 and 48, making 48 the 5th term), we can set up the equation 48 = 3 * r^4 and solve for r.

Doing so gives us r = (48/3)^(1/4) = 2.

Now that we have the common ratio, we can find the second inserted mean (which is the third term of the sequence, or a_3) using the formula a_3 = a_1 * r^(3-1) = 3 * 2^2 = 12.

So, the second inserted mean is 12, which corresponds to option b.

Question

To solve this problem, we need to use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

First, we need to find the common ratio (r). Since we know the first term (a_1 = 3) and the last term (a_5 = 48, because we have inserted 3 geometric means between 3 and 48, making 48 the 5th term), we can set up the equation 48 = 3 * r^4 and solve for r.

Doing so gives us r = (48/3)^(1/4) = 2.

Now that we have the common ratio, we can find the second inserted mean (which is the third term of the sequence, or a_3) using the formula a_3 = a_1 * r^(3-1) = 3 * 2^2 = 12.

So, the second inserted mean is 12, which corresponds to option b.

Knowee AI · Accepted Answer

To solve this problem, we need to use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

First, we need to find the common ratio (r). Since we know the first term (a_1 = 3) and the last term (a_5 = 48, because we have inserted 3 geometric means between 3 and 48, making 48 the 5th term), we can set up the equation 48 = 3 * r^4 and solve for r.

Doing so gives us r = (48/3)^(1/4) = 2.

Now that we have the common ratio, we can find the second inserted mean (which is the third term of the sequence, or a_3) using the formula a_3 = a_1 * r^(3-1) = 3 * 2^2 = 12.

So, the second inserted mean is 12, which corresponds to option b.

Three geometric means are inserted between 3 and 48. What is the second in the inserted means?Select one:a. 6b. 12c. 24d. 48

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Three geometric means are inserted between 3 and 48. What is the second in the inserted means?

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