B A S I C A R I T H M E T I C
1. (x − 2)2
+ (x − 9)2
= (x − 11)2
(± 6)
2. x+1
x+3
− x−1
x+5
= x(x−1)+12
x(x+8)+15
(1,4)
A R I T M E T I C P R O G R E S S I O N
3. Give the first six memebers of following aritmetic serie:
a1 + a4 + a6 = 71
a5 + a2 + a3 = 2
(5, 12, 19, 26, 33, 40)
4. x + 4x + 7x + 10x + . . . + 367x = 1468
(15.41689)
5. Find S1000
1 + 2 + 3 + . . . + 1000 =?
(500,500.00)
G E O M E T R I C P R O G R E S S I O N
6. Give the first three members of following serie:
A1 − A2 + A3 = 9
A4 − A5 + A6 = 72
(9, 6, 12)
7. You ride a bicycle over one week. You start on Monday and the first
day you ride 20 km. Up the next day you always ride 5 km more. How
many kilometers do you ride on Sunday and how many kilometers did
you ride after one week?
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(50, 245)
8. Solve the same example, but now your progress is always 5 % more to
the previous ride.
(26.802, 162.84)
9. You put 1 dollar on your bank account. At the end of avery year you
will obtain five cents as interest. How much you will have on your bank
account after seven years?
(1.35)
10. Solve the same example if the bank promise you to pay 5 % of your
current balance account.
(1.4071)
11. What will be the balance on your bank account if you save on April, 1
2018 CZC 1,0800,000.00 and on September, 1 2018 you will withdraw all
your deposit? The interest rate is 4.2 % p. a. and the bank calculates
interest once a year.
(CZC 1,098,900.00)
12. Solve the previous example applying the concept of compound interest.
(CZC 1,098,673.00)
13. How much you need to put on the bank account to obtain PLN 1,457,286.261
after 5.7 years? The annual interest rate corresponds to 5.5 % and the
bank calculates the interest once a year. MAXIMAMIZE THE UTIL-
ITY!
(PLN 1,073,683.00
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14. How long do you have to wait to obtain CZC 8,200.00 if you put on
your bank account CZC 4,561.00? Further, you know that the bank
has two interest periods in one year and the monthly interest rate is
0.4 %.
MAXIMAMIZE THE UTILITY!
(tcompound = 24.733478IPs, tcombined =
24, 731158, i.e. cca 12 years 4 months and 12 days)
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