SECT. 2.7GEOMETRIC SEQUENCES
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I) WHAT IS A GEOMETRIC SEQUENCE?
A sequence where each term after the first ismultiplied by a common ratio “r”
Not the same as an arithmetic sequence (Add)
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II) FORMULA FOR GEOMETRIC SEQUENCE:
The value of the “nth” term
Value of the 1st term
Common Ratio
The rank of the term
- Divide any term by its previous term
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EX: GIVEN THE FOLLOWING SEQUENCE,FIND THE 20TH TERM:
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EX: GIVEN THE FOLLOWING SEQUENCE,FIND OUT HOW MANY TERMS THERE ARE:
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EX: GIVEN THE THREE TERMS IN A GEOMETRICSEQUENCE, FIND THE COMMON RATIO:
To find the common ratio, you can just take any term and divide it by the previous term
So, the common ratio will be:
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EX: THE THIRD TERM OF A GEOMETRICSEQUENCE IS 27 AND THE SIXTH TERM IS 64.FIND THE COMMON RATIO:
Each term in the sequence is equal to theprevious term multiplied by the common ratio:
The sixth term is equal to both 64 and 27r3
To find the terms in between, just multiply 27
by the common ratio.
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EX: GIVEN AND FIND THECOMMON RATIO AND THE FIRST TERM:
Divide the
Equations!
The common
Ratio is 2/3 & -2/3
Now solve for
the first term
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EX: A RUBBER BALL IS DROPPED FROM A HEIGHT OF 10M.AFTER EACH BOUNCE, THE BALL RETURNS TO 57% OF ITSPREVIOUS HEIGHT. AFTER HOW MANY BOUNCES WILL THE BALLBOUNCE LESS THAN ½ A METER?
After 6 bounces, the ball will bounce less than ½ a meter
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HOMEWORK:
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