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Insert the indicated number of arithmetic means given the first and last term, show the solution.
1. -5 and 50 indicated number [6]
2. -12 and 12 indicated number [5]
3. 21 and -9 indicated number [4]
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I will solve parts (2) and (3).
I will show you a simple method and a simple mantra, which you will be able easy apply in many other cases you can meet.
PART (2)
Between the endpoints, -12 and 12, the distance is 24 units.
5 inserted arithmetic means divide this distance, this segment [-12,12], in 5+1 = 6 gaps of equal length.
The length of each such gap is 24/6 = 4 units, and it is the common difference of the arithmetic sequence.
Hence, the sequence is -12, -8, -4, 0, 4, 8, 12.
The arithmetic means which you INSERT are -8, -4, 0, 4 and 8.
Solved and completed.
PART (3)
Between the endpoints, -9 and 21, the distance is 30 units.
4 inserted arithmetic means divide this distance, this segment [-9,21], in 4+1 = 5 gaps of equal length.
The length of each such gap is 30/5 = 6 units, and it is the common difference of the arithmetic sequence.
Hence, the sequence is -9, -3, 3, 9, 15, 21.
The arithmetic means which you INSERT are -3, 3, 9 and 15.
Solved and completed.
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Do you see the repeating mantra and how it works ?
Now you know the method. Apply it in thousands other similar problems.