When you are doubling (or tripling or halving) a quantity, you are using the operation of multiplication (or division). When you do this repeatedly you form a geometric sequence.

Objective:

To identify and calculate terms in a geometric sequence.

Geometric Sequence – A sequence in which every number is a product of the previous number and a common ratio, r.

Example: 3, 6, 12, 24, ______

x2 x2 x2If is the current number in the sequence and is the previous term number, the common ratio, r, can be found by dividing:

r = In the example above = = 2…The common ratio is 2 This will work for

any term in a geometric sequence:

= = 2

The explicit formula for a geometric sequence then is:

Notice- each new term in a geometric sequence is represented by multiplying the one before. Remember repeated multiplication can be represented using _______________.

Example 1- Find the term13’th term; 8, -16, 32, -641) Find a common ratio using division:

=

2) Use the formula correctly to find

Stuff I know:r = -2

n = 13

Formula:

8’th term; 1, 4, 16, 64Check your work:Did you get 65536?

No? Good. A common mistake is to take the term number ,n, as the exponent instead of n-1.

The reason is that in order to get the first term in the sequence you have to raise it to the power of zero. That means the power of every term after, is one less then the term.

The correct answer is 16884

Example 2- Find the term

Another Example:

Find the 5’th and 10’th term of the sequence

-Compare your answer with at least 2 people to make sure you are getting it.

Challenge problem:A certain geometric sequence has the following relationship:

– = 60 and

1) Find and

2) Find the first term in the sequence (.

Source:Edmonds.com

I bought a car for $24,500.

1) I get buyers remorse and don’t want the car any more as soon as I get home. How much is the car worth if I bring it back?

2) The car turned out great but after 7 years I would like to upgrade to a new car. Assume 15% depreciation and decent condition. How much will I get for my car if I trade it in (what is the car worth)?

WordProblem

You have a coupon that let’s you save 5% off a Television that originally costs $1200.

There is no limit to how many coupons you can use and each coupon gives you another 5% off the last discounted price.

1) If you use 10 coupons what will the cost of the television be?

2) How many coupons will you need for the cost to be $1? Round your answer to the nearest coupon.

Word Problem