Homework Questions. Recursive v. Explicit Get out notes and get ready!

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Homework Questions

Recursive v. Explicit Get out notes and get ready!

Definition Recursive Formula – a sequence is recursively defined if the first term is given and there is a method of determining the nth tem by using the terms that precede it. English – if you can use the term before it to figure out what comes next Ex: {-7, -4, -1, 2, 5, …}

Examples of Recursive {-9, -4, -2, 0, 2, …} {-4, -8, -16, -32, -64, …} {6, 11, 16, 21, 26, …} {8, 4, 2, 1, …}

Application A ball is dropped from a height of 9 feet. It hits the ground and bounces to a height of 6 ft. On each rebound it rises 2/3 the height of the previous bounce. Write a recursive formula for the sequence that represents the height of the ball on each bounce. Create a table showing the height of the ball on each bounce. Find the height of the ball on the fourth bounce.

Application If the starting salary for a job is $20,000 and a raise of $2000 is earned at the end of each year of work, what will the salary be at the end of the 6 th year? Find a recursive formula to represent this problem and make a table of values to find the solution.

Definition Explicit Formula – a formula that allows direct computation for any term for a sequence English – you don’t need to term prior in order to figure out what the nth term is going to be. Ex: {8, 9, 10, 11, 12, …} a n = n + 7

Examples of Explicit {-3, 1, 5, 9, …} {1, 4, 9, 16, …} {7, 9, 11, 13, …} {24, 20, 16, 12, …}

Homework Worksheet 9-1