|Geometric Series: |
A fable says that a wise women solved a king's dire problem and the king said she could have anything she wanted in return. She demurely asked only for a chessboard with 1 grain of wheat on the first square, 2 on the second, 4 on the third, 8 on the Fourth and so on up to sixty-fourth square.
- Find a formula for the nth term of the arithmetic sequence: -2, -8, -14, -20, .....
- Calculate the missing terms in the arithmetic sequence, if a1 = 6, and a5 = 66.
Kim's starting salary was $40,000 per year. Each year we receive a cost of living adjustment (COLA) of three percent of our original salary. Write a sequence showing my salary for my first five years of working here.
a1 = 40,000
a2 = 40,000(1.03) = 41,200
a3 = 41,000(1.03) = 40,000(1.03)2 = 42,436
a4 = 40,000(1.03)3 = 43,709.08
a5 = 40,000(1.03)4 = 45,020.35
Determine the amount required in an individual retirement account for an individual who retires at age 65 and wants an income of $2000 from the account each month for 20 years. Assume that the account earns 9% compounded monthly.
P = W(1+r/12)-1 + W(1+r/12)-2 + ..............W(1+r/12)-12t
The initial deposite is given by
P = W (12/r) [1- (1+r/12)-12t
A company is offering a job with a salary of $30,000 for the first year. Suppose that during the next 39 years, there is a 5% raise each year. Determine the total compensation over the 40 year period.
A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet.
a) Find the total distance travelled by the ball
b> The ball takes the following time for each fall
s1 = -16t2 + 16, s1 = 0 if t = 1
s2 = -16t2 + 16(0.81), s2 = 0 if t = 0.9
s3 = -16t2 + 16(0.81)2, s3 = 0 if t = 0.92
s4 = -16t2 + 16(0.81)3, s4 = 0 if t = 0.93
sn = -16t2 + 16(0.81)n-1, sn = 0 if t = 0.9n-1
beginning with s2 the ball takes the same amount of time to bounce up as it does to fall, and thus the total time elapsed before it comes to rest is
t = 1 + 2 sigma(n=1 to infinity) (0.9)n
Find this total.
a) 152.42 feet
b) 19 seconds
Directions: Answer the following questions. Also write at least 5 examples of your own.