Homework Questions
Recursive v. Explicit
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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, …}

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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 6th 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, …}
 an= n + 7
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Examples of Explicit

{-3, 1, 5, 9, …}
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{1, 4, 9, 16, …}

{7, 9, 11, 13, …}

{24, 20, 16, 12, …}
Homework

Worksheet 9-1