Insert three arithmetic means between 4 and 16. What is the largest of the means?Select one:a. 7b. 10c. 13d. 16
Question
Insert three arithmetic means between 4 and 16. What is the largest of the means?
Select one:
- a. 7
- b. 10
- c. 13
- d. 16
Solution
To insert three arithmetic means between 4 and 16, we first need to find the common difference (d). The formula for the common difference in an arithmetic sequence is d = (b - a) / (n + 1), where a and b are the first and last terms, and n is the number of means.
Here, a = 4, b = 16, and n = 3.
So, d = (16 - 4) / (3 + 1) = 12 / 4 = 3.
The arithmetic means are then a + d, a + 2d, and a + 3d.
So, the three arithmetic means are 4 + 3 = 7, 4 + 23 = 10, and 4 + 33 = 13.
Therefore, the largest of the means is 13.
So, the answer is c. 13.
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