Grade 10 IGCSE Math Extended Sequences A set of numbers listed in a specific order, and the numbers can be found using a specific rule. Number sequence: The first term is denoted by , the second by , the third by , and so on. The th term is denoted as . What rule does this number sequence follow? For example:

1, 4, 7, 10, ...

is a number sequence. Each term differs from the previous one by the same constant number Example 1 Instead of using words, we can use algebra to define rules for number sequences. is the rule to find ANY term in a number sequence. This is why is often called the general term. Just take the number of the term you want and plug it in for n, and voila, you get that term in the sequence. Big Idea:

Using Algebra to Define Sequences PRACTICE Work on Exercise 26A on pg. 535 The algebraic rule for our sequence of 1, 4, 7, 10, ... would be . BONUS: What number set does n belong to? Example 3 Example 2 Example 4 PRACTICE Work on Exercise 26B on pg. 537 Geometric Sequences Geometric sequence - each term is found by multiplying the previous term by the same constant number. Linear sequence - 2, 6, 18, 54, ... is a geometric sequence. Big Idea: Finding the nth term. Linear Sequences Geometric Sequences 1, 4, 7, 10, ... Linear sequence Repeated addition Multiplication So 2, 6, 18, 54, ... Geometric Sequence Repeated Multiplication Exponents So Example 5 Example 6 PRACTICE Work on Exercise 26C on pg. 538 The Difference Method In your exploration, you discovered the power of the difference method to help you find general rules for sequences. Let's practice it a bit more. Example 7 Example 8 Example 9 PRACTICE Work on Exercise 26D on pg. 543 Finding the General Term with your GDC 1. You still need to make a difference table to determine what kind of sequence you're dealing with. For quadratic and cubic sequences, using your calculator to find the general term can sometimes be faster.

Let's practice with the sequence from Examples 8 and 9. 2. Enter the first two rows (say L1 and L2) as lists in your calculator. 3. From our table, we know this is a quadratic sequence. So perform a quadratic regression (STAT) with L1 and L2. For a cubic sequence, the process is the same, except choose cubic regression. Take a moment to review your Investigation and add these terms to your Vocabulary Bank: quadratic sequence

cubic sequence

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# Grade 10 IGCSE Extended - Sequences

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