Arithmetic progression

Question

row 1                          1

row 2                       3    5

row 3                    7    9   11

row 4                13  15   17  19

row 5             21  23   25  27  29

            

Question A. What is the sum of the numbers on row 6?

Question B. What is the sum of the numbers on row 100?

Question C. What is the sum of all numbers on row n?

Answer 1

Ok. The first thing I do is add up the rows I have. Here's my list of answers:

 

row 1: 1

row 2: 8

row 3: 27   Oh, I'm seeing a pattern. So far they are the cubes of the row numbers, that is, n^3.

row 4: 64

row 5: 125 

 

Yep, cubes.

 

So, I expect row 6 to be 6^3, which is 216. I check it by writing it out and adding and yes, it's 216.

Thankfully, I can just figure out 100^3 without writing all the numbers, and then write my answer for the last question, and so can you!

 

--Louise K