perplexus.info :: Numbers : Arithmetic Sequence Crossed Digital Root Puzzle

Arithmetic Sequence Crossed Digital Root Puzzle (Posted on 2023-02-16)

A, B, and C are three consecutive integer terms (in this order) of an arithmetic sequence with nonzero common difference d.
Define:
• x = A³+B³+C³
• d(x) as the digital root of x.

Determine d(x), given that x is NOT a multiple of 3.

See The Solution Submitted by K Sengupta

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Huh?

| Comment 1 of 3

Let A = n-d, B = n, C=n+d

Then x = (n-d)^3 + n^3 + (n+d)^3 = 3n^3 + 6nd^2

But this makes x a multiple of 3

Have I gone wrong somewhere?

Posted by Steve Herman on 2023-02-16 07:45:02

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