#### Question

# CAPE/A-level math Question please help! series and sequences?

a car was purchased at the begining of the year for P dolars. the value of the car at the end of each year is estimated to be the value at the begining of the year multiplied by ( 1 - 1/q ), where q is a Natural number.

1- determine in terms of P and q the value of the car 'n' years after purchase.

2- if the original value of the car was $20000 and the value of the car at the end of the 4th year was $8192.00 find: (i) the value of q (ii) the estimated value of the car after 5 years.

when i tried to work this i got a decimal # for q so my answer is wrong. please show me all the steps please n thank you!

#### Answers

1. P(1 - (1/q))^n

2i.

20000 * (1 - (1/q))^4 = 8192

(1 - (1/q))^4 = 8192 / 20000

(1 - (1/q))^4 = 0.4096

1 - (1/q) = (0.4096)^(1/4)

1 - (1/q) = 0.8

-1/q = 0.8 - 1

-1/q = -0.2

1/q = 0.2

q = 1/0.2

q = 5

2ii.

20000 * (1 - (1/5))^5

= 20000 * (1 - 0.2)^5

= 20000 * 0.8^5

= 20000 * 0.32768

= $6,553.60