Final answer:
The sequence of 5 arithmetic means between 14 and 86 is 26, 38, 50, 62, and 74. The common difference is found by dividing the range by the number of intervals, which in this case is 12.
Step-by-step explanation:
To insert 5 arithmetic means between 14 and 86, we first need to determine the common difference in the arithmetic sequence. We do this by taking the difference between the two given terms and dividing by the total number of intervals between them, which is the number of arithmetic means plus 1. The number of intervals here is 5 (arithmetic means) + 1 = 6. Now, the common difference (d) can be calculated as:
d = (86 - 14) / 6 = 72 / 6 = 12
Now, we'll use this common difference to find each arithmetic mean:
- First arithmetic mean: 14 + 12 = 26
- Second arithmetic mean: 26 + 12 = 38
- Third arithmetic mean: 38 + 12 = 50
- Fourth arithmetic mean: 50 + 12 = 62
- Fifth arithmetic mean: 62 + 12 = 74
Therefore, the sequence of 5 arithmetic means between 14 and 86 is 26, 38, 50, 62, 74.