algebra question?

Question

these questions has to do with arthmetic and geometric formulas and i dont really know which ones to use, or what numbers to put where. PLEASE HELP!!! #1 You save $1200 this year. You plan to save $1000 more each year than the year before. How much would you dave the 3rd year? How much would you save the 20th year? (im pretty sure its the explicit formula but i dont know know if its arithmetic or geometric) #2 A Certain Company had a sales increase of 3%. Assume the increase will continue at the same rate. a) write a recursive formulafor the amount of sales. b)Write an explicit formula for sales if the first years were $2.5 million. c) predict sales for the 3rd year. These next two are just haveing to find the missing terms... please tell me how u figured it out #1 Arithmetic : -36,___,___,___,-8 #2 Geometric : 32,___,200

Answer 1

Last question:

-36 + 4d = -8 (d is the common difference)
4d = 28
d = 7

So your sequence is -36, -29, -22, -15, -8 (just keep adding 7)

32*r^2 = 200 (r is common ratio)

r^2 = 200/32 = 100/16 = 25/4
r = +/-(5/2)

So the sequence multiplies 32 by either 5/2 or -5/2, giving you 2 possible answers:

32, 80, 200 or 32, -80, 200

Answer 2

#1 Use this formula: 1000x+1200

So in 3 years, it would be $4200 and in 20 it would be $21,200.

#2 I don't remember anything about recursive or explicit formulas, but I think a should be x+0.03xy where x is the earnings of the first year and y the number of years after, b should be $2,575,000, and c should be 2,725,000. I think that's right, hope that helped.

Answer 3

For increasing cubic binomials the generic formulation is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D