Open Question: insert three numbers between 5 and 10 so that all five numbers are in arithmetic sequences?
Let a[n] be the sequence.
Then a[n] = a[1] + (n-1)d where d is the common difference.
a[1] = 5
10 = a[5] = a[1] + 4d = 5 + 4d
4d = 5
d = 1.25
So the sequence is
5, 6.25, 7.50, 8.75, 10
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