Can you help me with figuring out the formula I need to use for this problem? (Recursive/Explicit/Something else?)

Question

Ronny is building a Lego pyramid. The base of the pyramid has 75 blocks. Each row of the pyramid contains 2 fewer blocks than the row below it. The top row has only 1 block. How many rows are in the pyramid?

Answer 1

With word (story) problems, the first thing you should do is read and re-read the problem until you understand it and can put it into your own words.  This also helps to eliminate TMI (too much information), to identify "bricks to stumble over" (like multiple units, so conversion is required) and to identify "brick walls to run into" (like not knowing the definition or the formula).

 

Here is my re-wording:  A pyramid has 1 block on the top, then 2 additional blocks on each lower row.  How many rows are needed to have 75 blocks on the base?

 

The sequence is:   1,  3,   5,   7,  ...

 

This is an arithmetic sequence.  The n^th value is [a₁ + (n-1)d], where d=common difference.

Here, d=2, so what is n when:

    a_n = a₁ + (n-1) d  = 75                    [note a₁=1,  d=2]

           1  + (n-1)(2) = 75

           1 + 2n - 2 = 75

             2n = 76

              n = 38

 

The pyramid has 38 rows.