Question 348207
<pre><b>
2,20,10,100,50

2*10 = 20
       ||
       20/2 = 10
              || 
              10*10 = 100
                      |||
                      100/2 = 50<font color = "red">
                              ||
                              50*10 =500</font> 
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

a<sub>1</sub> = 2

To find a<sub>2</sub>, since 2 is even, we multiply the preceding 
odd-numbered term a<sub>1</sub>, which is 2, by 10:

a<sub>2</sub> = a<sub>1</sub>*10 = 2*10 = 20

To find a<sub>3</sub>, since 3 is odd, we divide the preceding 
even-numbered term a<sub>2</sub>, which is 20, by 2:

a<sub>3</sub> = a<sub>2</sub>/2 = 20/2 = 10

To find a<sub>4</sub>, since 4 is even, we multiply the preceding 
odd-numbered term a<sub>3</sub>, which is 10, by 10:

a<sub>4</sub> = a<sub>3</sub>*10 = 10*10 = 100

To find a<sub>5</sub>, since 5 is odd, we divide the preceding 
even-numbered term a<sub>4</sub>, which is 100, by 2:

a<sub>5</sub> = a<sub>4</sub>/2 = 100/2 = 50
<font color = "red">
To find a<sub>6</sub>, since 6 is even, we multiply the preceding 
odd-numbered term a<sub>5</sub>, which is 50, by 10:

a<sub>6</sub> = a<sub>5</sub>*10 = 50*10 = 500
</font>

Edwin</pre>