1. Sequences Practice Questions (Pearson Chapter 3) Ex 3.2: 11, 12 p85

Sequence Definitions A sequence can be defined in any of the following ways: The first few terms are listed and you assume the pattern continues indefinitely Eg 34, 27, 20, 13, .... A word description is given Eg Start with 2 and add 5 each time A general formula is given which represents the general term (called the nth term) Eg {2n + 1) generates the sequence 3, 5, 7, 9 ....... (note: your text calls the ”general formula” the “explicit formula”)

Arithmetic Sequences where n = the number of the term d = the common difference u1 = the first term un = the general term (or nth term)

Arithmetic Sequences Examples Consider the sequence: 2, 9, 16, 23, 30, .... 2. An arithmetic sequence has a first term of 120 and a 10th term of 57. Find the 15th term. Show that the sequence is arithmetic Find the formula for the general term Find the 100th term of the sequence Are 828 and 2341 in this sequence?

Arithmetic Sequences Examples A car whose original value was $25600 decreases in value by $90 per month. How long will it take before the car’s value falls below $15000? 4. Find the number of terms in the arithmetic sequence 84, 81, 78, ...... 12

Geometric Sequences where n = the number of the term r = the common ratio u1 = the first term un = the general term (or nth term)

Geometric Sequences Examples 6. Find the number of terms in the geometric sequence 0.25, 0.75, 2.25, ....., 44286.75 5. a) Find the fifteenth term in the sequence 200, 20, 2, 0.2, .... b) Find the eleventh term in the sequence 7. The number of people in a small country town increases by 2% per year. If the population at the start of 1970 was 12500, what is the predicted population at the start of the year 2020?

Geometric Sequences Examples 8. A geometric sequence has a fifth term of 3 and a seventh term of 0.75. Find the first term, the common ratio and the tenth term. A car originally worth $34000 loses 15% of its value each year. Write a geometric sequence that gives the year by year value of the car. Find the value of the car after 6 years After how many years will the value of the car fall below $10000?