SOLUTION: describe the pattern in the numbers 2,20,10,100,50 and list the next number

2,20,10,100,50

2*10 = 20
       ||
       20/2 = 10
              || 
              10*10 = 100
                      |||
                      100/2 = 50
                              ||
                              50*10 =500 
The pattern is: 

1. Start with 1st term 2.
2. To find an even numbered term, multiply the preceding 
   odd-numbered term by 10.
3. To find an odd numbered term, divide the preceding 
   even-numbered term by 2.  

We start with

a1 = 2

To find a2, since 2 is even, we multiply the preceding 
odd-numbered term a1, which is 2, by 10:

a2 = a1*10 = 2*10 = 20

To find a3, since 3 is odd, we divide the preceding 
even-numbered term a2, which is 20, by 2:

a3 = a2/2 = 20/2 = 10

To find a4, since 4 is even, we multiply the preceding 
odd-numbered term a3, which is 10, by 10:

a4 = a3*10 = 10*10 = 100

To find a5, since 5 is odd, we divide the preceding 
even-numbered term a4, which is 100, by 2:

a5 = a4/2 = 100/2 = 50

To find a6, since 6 is even, we multiply the preceding 
odd-numbered term a5, which is 50, by 10:

a6 = a5*10 = 50*10 = 500


Edwin