y = 2x + ? Lesson: Linear and Recursive patterns objective: To find the nth term in a linear pattern. nth term is the expression that can be used to find any term in a sequence. (Often written as y = ax +b) or ax + c. EX: Find the nth term Write answer in function form y = ax + b x y 1 3 2 5 7 4 9 The difference in the y column tells us the coefficient of the x y = 2x + ? To find the missing number from here, multiply everything in column 1 by 2 and find its common difference with column 2.

-22 y = -3x + 8 Find y when x = 10... the 10th term EX: x y 1 5 2 3 -1 4 -4 Common difference is -3. y = -3x + ? y = -3x + 8 Find y when x = 10... the 10th term -22

Write the first four terms of the sequence: a1 = -4 an = an-1 + 5 Recursive Sequences Recursion is the process of choosing a starting term and repeatedly applying the same process to each term to arrive at the following term.  Recursion requires that you know the value of the term immediately before the term you are trying to find. Write the first four terms of the sequence:  a1 = -4   an = an-1 + 5 Example: a1 = -4 n = 2: a2 = a2-1 + 5 = 1 n = 3 a3 = a3-1 + 5 = 6 n = 4 a4 = a4-1 + 5 = 11 In recursive formulas, each term is used to produce the next term.  Follow the movement of the terms through the set at the left. n 1 2 3 4 an-1 +5 -4 6 11 Solution:

Example: a1 = 4 an = an-1 – 7 Write the first four terms of the recursive sequence. -3 a2 = a2 – 1 – 7 a = 4 – 7 n = 2 -10 a3= a3 – 1 – 7 a = -3 – 7 n = 3 -17 a4 = a4 – 1 – 7 a = -10 – 7 n = 4