3 squares with measurements of 2x2, 3x3 and 4x4. do these lengths only not the widths represent an arithmetic sequence? what would be a recursive or explicit formula for this?

Question

3 squares with measurements of 2x2, 3x3 and 4x4.  do these lengths only not the widths represent an arithmetic sequence? what would be a recursive or explicit formula for this?

whpalmer4 · Answer

An arithmetic sequence has a common difference between adjacent terms.  Evaluate 3*3-2*2, and 4*4 - 3*3.  Are they the same value?  If not, it isn't an arithmetic sequence.

anonymous · Answer

no they aren't.  What if I only consider the lenghts not the widths then it would be an arithmetic sequence?

whpalmer4 · Answer

Sorry, I didn't read that correctly.  Yes, the lengths are an arithmetic sequence:

3-2 = 1
4-3 = 1