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Answer:
See Below.
Step-by-step explanation:
The first three terms of an A.P is equivalent to the first three terms of a G.P.
We want to show that this is only possible if r = 1 and d = 0.
If a is the initial term and d is the common difference, the A.P. will be:
Likewise, for the G.P., if a is the initial term (and it does not equal 0) and r is the common ratio, then our sequence is:
The second and third terms must be equivalent. Thus:
We can cancel the d. Multiply the first equation by -2:
We can now add this to the second equation:
Simplify:
Now, we can divide both sides by a (we can do this since a is not 0):
So:
Factor:
Thus:
The first equation tells us that:
Therefore:
Hence:
Q.E.D.