 A mysterious illness is affecting the residents of Mexico city. DAYNUMBER OF PEOPLE INFECTED FIRST DAY8 SECOND DAY24 THIRD DAY72

 The people infected as the days go by:  8, 24, 72, 216, 648, … How many people will get infected in the 6th day? WHY???

Fibonacci considered the growth of an idealized (biologically unrealistic!!!) rabbit population

Newly born pair of rabbits: one male and one female = 1 pair

= 2 pairs

 A mating pair always produces one new pair (one male, one female) every month from the second month on…  How many pairs will there be in one year?

 Month 0: = 1 pair  Month 1: = 1 pair  Month 2: = 2 pairs  Month 3: = 3 pairs  Month 4: = 5 pairs

 1, 1, 2, 3, 5, 8,13, 21, 34, …  What is the next number? WHY???

A company began doing business four years ago. Its profits for the last four years have been $11 million, $15 million, $ 19 million and $23 million. If the PATTERN continues the expected profit in 30 years is going to be: $127 million WHY????

All of the above are… SEQUENCES

 A SEQUENCE is a set of quantities arranged in a definite order. For example:  1, 2, 3, 4, 5, …  1, 4, 9, 16, 25, …  1, 8, 27, 64, 125, …  -10, -8, -6, -4, -2, …

Arithmetic Sequence 1, 3, 5, 7, 9, … 11, 15, 19, 23, … Geometric Sequence 2, 6, 18, 54, , 20, 2, 0.2

An arithmetic sequence will always have a common difference between successive terms. For example:  2, 4, 6, 8, 10, …COMMON DIFFERENCE of 2  1, 4, 7, 11, 14, …COMMON DIFFERENCE of 3

How can you calculate the 30 th term? Moreover, how can you calculate the n th term? Hint: What is the common difference? YEARSPROFIT 111 mm 215 mm 319 mm 423 mm …… 30????

YEARSPROFIT 111 mm 215 mm 319 mm 423 mm … 30 The common difference is – 11 = 4 19 – 15 = 4 Therefore we know that we need to multiply the n th times 4

But … 4(1) = 4, 4(2) = 8 and 4(3) = 12 … If we add + 7 we’ll get the result. Hence, in 30 years the profit will be 30(4) + 7 = YEARSPROFIT 111 mm 215 mm 319 mm 423 mm … mm

HINT: Look for it in your booklet!!!!!

A geometric sequence will always have a common ratio between successive terms. For example:  2, 4, 8, 16, 32, …COMMON RATIO of 2  3, -9, 27, -81, 243, …COMMON RATIO of -3

 A mysterious illness is affecting the residents of Mexico city. DAYNUMBER OF PEOPLE INFECTED FIRST DAY8 SECOND DAY24 THIRD DAY72

DAYNUMBER OF PEOPLE INFECTED FIRST DAY8 SECOND DAY24 THIRD DAY72 …… 20th DAY??? How can you calculate the 20 th term? Moreover, how can you calculate the n th term? Hint: What is the common ratio?

DAYNUMBER OF PEOPLE INFECTED FIRST DAY8 SECOND DAY24 THIRD DAY72 …… 20th DAY9,298,091,736 The common ratio is 3 8x3= 24 8x3x3 = 72 8x3x3x3 =216 Therefore we know that we need to multiply 8x3x3x…x3 19 times

HINT: Look for it in your booklet!!!!!

 Your parents give you an allowance of 5 euros (!!!) a week when you are 5 years old. Every year your allowance is increased by 1 euro. You receive an allowance every week until your 21st birthday.  Your parents give you an allowance of 5 euros (!!!) a week when you are 5 years old. Every year your allowance is increased by 12%. You receive an allowance every week until your 21st birthday.