A three-digit even number is given such that the hundreds, tens, and unit digits respectively form a decreasing arithmetic sequence. When two is added to the number, the same order of the digits now forms a geometric sequence. What is the original number?
A three-digit even number is given such that the hundreds, tens, and unit digits respectively form a decreasing arithmetic sequence. When two is added to the number, the same order of the digits now forms a geometric sequence. What is the original number?
840 will work. Arithmetic sequence, the difference is –4
842 Geometric sequence, the multiplier is 1/2
I complain about people who give only the answer, without explaining the steps which led to that answer.
Sorry; I have no steps. I just contemplated this for a little while and an answer sort of fell out of the sky.
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+36916 840 arithmetic series d = 4
842 geometric series r = 1/2
840 is the original number
