The document discusses geometric sequences, which are sequences where each term is found by multiplying the previous term by a common ratio. It provides an example of a geometric sequence and shows how to calculate terms using the common ratio and explicit formula. It also discusses identifying the common ratio using division and using the explicit formula to find specific terms in a geometric sequence.

1. 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.

2. 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 x2
If 𝑎 𝑛 is the current number in the sequence and 𝑎 𝑛−1 is the previous term
number, the common ratio, r, can be found by dividing:
r =
𝑎 𝑛
𝑎 𝑛−1
In the example above
𝑎 𝑛
𝑎 𝑛−1
=
6
3
= 2
…The common ratio is 2
This will work for any
term in a geometric
sequence:
𝑎 𝑛
𝑎 𝑛−1
=
24
12
= 2

3. 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 _______________.

4. 1) Find a common ratio using division: 𝑟 =
𝑎 𝑛
𝑎 𝑛−1
r =
𝑎 𝑛
𝑎 𝑛−1
=
−16
8
= −2
2) Use the formula correctly to find 𝑎13
Stuff I know:
r = -2
𝑎1 = 8
n = 13
Formula:
𝑎13 = 𝑎1 ∗ 𝑟 𝑛−1 → 8 ∗ (−2)13−1
→ 𝑎13= 8 ∗ (−2)12
→ 𝑎13= 8 ∗ (−2)12
→ 𝑎13= 8 ∗ 4096
→ 𝑎13= 32768

5. Check 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

6. 𝑎1 = 8 𝑎𝑛𝑑 𝑟 = 3
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.

7. A certain geometric sequence has the following relationship:
𝑎5 – 𝑎3 = 60 and
𝑎5
𝑎3
= 16
1) Find 𝑎3 and 𝑎5
2) Find the first term in the sequence (𝑎1).

8. 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)?

9. 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.