A) Write an equation for the sequence: 

n 1 2 3 4 an 3125 2500 2000 1600

an =  

B) Use your equation from part A to find the 20th term of the sequence. *Round your result to the nearest hundredth (2 decimal spots)
a20 =  


C) Use your equation from part A to find the first term number when an<10. (In other words, what is the term number - term numbers are whole numbers - when the term value first becomes less than 10?)

n =   

How many of the first ten numbers of the sequence 121, 11211, 1112111,... are prime numbers? 

The point lies on the curve .

1. If is the point use your calculator to find the slope of the secant line ( correct to six decimal places) for the following values of .

   1. 1.5

   2. 1.9

   3. 1.99

   4. 1.999

   5. 2.5

   6. 2.1

   7. 2.01

   8. 2.001

2. Using the results of part (a), guess the values of the slope of the tangent line to the curve at .

3. Using the slope from part (b), find an equation of the tangent line to the curve at .

The point lies on the curve .

1. If Q is the point , use your calculator to find the slope of the secant line PQ ( correct to six decimal places) for the following values.

   1. 0

   2. 0.4

   3. 0.49

   4. 0.499

   5. 1

   6. 0.6

   7. 0.51

   8. 0.501

2. Using the results of part (a), guess the value of the slope of the tangent line to the curve at

3. Using the slope from part (b), find an equation of the tangent line to the curve at .

4. Sketch the curve, two of the secant lines, and the tangent line.