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?

Guest Dec 29, 2021

#1**0 **

*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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Guest Dec 29, 2021

#2**0 **

840 arithmetic series d = 4

842 geometric series r = 1/2

840 is the original number

ElectricPavlov Dec 29, 2021