Quarter 1 Math 10 Lesson about Geometric Sequence

Quarter 1 Math 10 Lesson about Geometric Sequence

1. Geometric Sequences

2. Divide and Conquer
Findtheratioofthesecondnumbertothe
firstnumber.
2,8
Answer: 4

3. -3, 9
Answer: -3

4. 1, ½
Answer: ½

5. -5, -10
Answer: 2

6. 12, 4
Answer: 1/3

7. -49, 7
Answer: -1/7

8. ¼, ½
Answer: 2

9. a
2
, a
3
Answer: a

10. k –1,k
Answer: k
k -1

11. 3m, 3mr
Answer: r

12. Activity: Fold Me Up!
Do the activity with a partner. One of you will perform the
paper folding while the other will do the recording in the
table.
1.Start with a big square from a piece of paper. Assume
the area of the square is 64 square units.
2.Fold the four corners to the center of the square and
find the area of the resulting square.
3.Repeat the process three times and record the results
in the table below.
Square 1 2 3
Area

13. Analysis
•Whatistheareaofthesquareformedafterthe
firstfold?Secondfold?Thirdfold?
•Isthereapatternintheareasobtainedafter3
folds?
•Youhavegeneratedasequenceofareas.What
arethefirst3termsofthesequence?
•Isthesequenceanarithmeticsequence?Why?
•Usingthepatternintheareas,whatwouldbe
the6
th
termofthesequence?

14. Geometric Sequence
A geometric sequence is a sequence
where each term after the first is obtained
by multiplying the preceding term by a
nonzero constant called the common
ratio.
The common ratio, r, can be
determined by dividing any term in the
sequence by the term that precedes it.

15. Examples
1.2,6,18,54,162,486,1458,...
2.12,−6,3,−3/2,3/4,…

16. Activity: “I’ll Tell You What You Are
Statewhethereachofthefollowing
sequencesisgeometricornot.
1.5,20,80,320,…
2.7√2,5√2,3√2,√2,…
3.5,-10,20,-40
4.1,0.6,0.36,0.216,…
5.10/3,10/6,10/9,10/15
6.4,0,0,0,0,…

17. Quiz

18. Assignment
Determine if the sequence is geometric. If it
is, find the common ratio.
1.-1, 6, -36, 216, …
2.-1, 1, 4, 8, …
3.4, 16, 36, 64, …
4.-3, -15, -75, -375, …
5.-2, -4, -8, -16, …