Number Pattern

Question

Row 1                3

Row 2              8 10
Row 3           15 17 19
Row 4         24 26 28 30
Row 5       35 37 39 41 43

 

Write an equation that can be used to find d, the difference between the last number and the first
number, for any row r.

Answer 1

For any row r the difference between 

the 1st and last terms is given by:

 

 d = 2(r-1)

 

In row 2 the difference between

1st and finsl term is 2(2-1) = 2

 

In row 3 the difference is

2(3-1) = 2(2) = 4

 

In row 4 the difference is 

2(4-1) = 2(3) = 6

 

And so forth.   Ascending multiples of 2.

 

For row 51 the difference would be

2(51-1) = 2(50) = 100