problem: how many rods does it take to create the 4th, 5th, nth steps using rods

Question

problem:

how many rods does it take to create the 4th, 5th, nth steps using rods as illustrated for two steps, which shows that 10 rods are needed for two steps.

And what is the equation that will generate the nth step. I.e how many rods does it take to create the nth step?

      XXX
      X X

XXX XXX
X X X
XXX XXX

Each XXX is a rod.

But this problem is from a linear algebra problem set, for which only linear solutions are assumed to be the desired answers. I understand that a quadratic answer makes sense, but the teacher assures me that this problem does not require a quadratic solution, only a linear one. [Can the teacher be wrong? I suppose, it happens! ;) ]

Thanks very much for any help on this!

Explanation / Answer

The data given is:
      Steps 1    2     3 4
      Rods 4   10   18 28

a(n)=2*n+a(n-1)+2   with a(0) = 0

a(1) = 2*1 + 0 + 2 = 4

a(2) = 2*2 + 4 + 2 = 4 +4+2 = 10

a(3) = 2*3 + 10 + 2 = 6 + 10 + 2 = 18

a(4) = 2*4 + 18 + 2 = 8 + 18+ 2 = 28

this is what your professor expecting.....?

above equation is linear in n   ?

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