Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

1) Find the sum of … to 12 terms Geometric Sum – G.2

2) Find the sum ofto 11 terms Geometric Sum – G.2

3) A geometric sequence has all its terms positive. The first term is 7 and the third term is 28. (a)Find the common ratio. (b)Find the sum of the first 14 terms. Geometric Sum – G.2

4) The first term of an arithmetic sequence is –16 and the eleventh term is 39. Calculate the value of the common difference. Review

5) The third term of a geometric sequence is 12 and the fifth term is All the terms in the sequence are positive. Calculate the value of the common ratio. Review

6) Consider the geometric sequence 8, a, 2,… for which the common ratio is (a)Find the value of a. (b)Find the value of the eighth term. (c)Find the sum of the first twelve terms. Review

Compound Interest Consider: – You invest $1000 in the bank – You leave the money in the bank for 3 years – You are paid an interest rate of 10% p.a. – The interest is added to your investment each year. Section 12EF – Word Problems

1) €6000 is invested at 5% p.a. simple interest for 15 years. Calculate the value of the investment at the end of this period.

2) $5000 is invested at 7% p.a. compound interest, compounded annually. What will it amount to at the end of 4 years? 10 years?

3) Dana has $25000 to invest at 9% p.a. for a 3 year period. What will her investment amount to if the interest is paid into her account: a) each quarter? b) each month?

4) How much should I invest now if I want the maturing value to be $ in 4 years’ time, if I am able to invest 8.5% p.a. compounded annually?

5) Ryan is a cartoonist, his comics have been bought by a newspaper, so he sends them the 28 comics he has drawn so far. Each week after the first he mails 3 more comics to the newspaper. a)Find the total number of comic strips sent after 1, 2, 3 and 4 weeks. b)Find the number of comic strips sent after 15 weeks. c)When does Ryan send his 120 th comic strip?

6) The initial population of rabbits on a farm was 50. The population increased by 7% each week. a)How many rabbits were present after 15 weeks? 30 weeks? b)How long would it take for the population to reach 500?

7) A basketball is dropped vertically. It reaches a height of 2 meters on the first bounce. The height of each subsequent bounce is 90% of the previous bounce. a)What height does it reach on the 8 th bounce? b)What is the total vertical distance traveled by the ball between the first and sixth time the ball hits the ground?

8) Each section of a soccer stadium has 44 rows with 22 seats in the first row, 23 in the second row, 24 in the third row, and so on. How many seats are there a)in row 44? b)in a section c)at a stadium which has 25 sections?

Homework Pg – Section E – #1-4, 7 Pg 411 – Section F – #1, 3, 4