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Geometric
Mean
As law-abiding citizens of the
Philippines and to promote the health
and safety standards, the Baliwag
Transit Inc., uses a kind of sequence
for their passengers’ queue cards as
they wait in line before riding in the
bus. This is done as part of the social
distancing policy of the government as
a way of preventing the spread of
COVID-19.
While distributing the number
cards, the dispatcher noticed
that there were missing number
cards. Mr. and Mrs. Ponce were
the first people in line, so they
decided to help the dispatcher.
They recalled how their children
were named.
2,4,_,_,32
We used the date of our
anniversary (February 2,
2002) in naming our
firstborn child. Then, we
used it as a multiplier to
derive the names of our
succeeding children.
The first and the last
terms of a geometric
sequence are called
extremes, and the terms
in between are called
geometric means.
Determining the
Geometric Mean
To insert one geometric
mean between geometric
extremes, use the mean
proportionality formula
given by: ±√𝑎𝑏 where: a
and b are the geometric
extremes
Examples: Insert the
missing geometric mean.
Use the mean proportionality
formula. Substitute the geometric
extremes. Solve for the
geometric mean. ±√𝑎𝑏 = ±√(5)(20)
= ±√100 = ±𝟏𝟎 ∴ There are two
possible answers for the
geometric mean, 10 or -10.
Use the mean proportionality
formula. Substitute the geometric
extremes. Solve for the
geometric mean. ±√𝑎𝑏 =
±√(48)(192) = ±√9216 = ±𝟗𝟔 ∴
There are two possible answers
for the geometric mean, 96 or 96.
Test what you know! Find the
geometric mean/s in the given
sequences.
1. 15, ___, 735
2. 9, ___, ___, -576
Finding the nth term
of geometric
sequence
Examples: Find the specified
term for each geometric
sequence.
1. 12, 60, 300, … 7th term
2. 𝑎1 = 19 r = -2 find 𝑎6
Test what you know! Solve for
the specified term of the
following geometric sequence.
1. 1, -9, 81, … 10th term
2. 𝑎1 = −8 r = 4 find 𝑎9
Test what you know! Solve for
the specified term of the
following geometric sequence.
1. 1, -9, 81, … 10th term
2. 𝑎1 = −8 r = 4 find 𝑎9
Examples: Find the sum of the
first n terms as indicated in
the following geometric
sequence.
1. 8, 16, 32, … sum of the
first 10 terms
2. 3, 3, 3, … sum of the first
100 terms
3. 17, -17, 17, … sum
of the first 200 terms
4. -23, 23, -23, …
sum of the first 301
terms
3. 17, -17, 17, … sum
of the first 200 terms
4. -23, 23, -23, …
sum of the first 301
terms
Examples: Determine if each
infinite geometric sequence
has a sum. If there is,
calculate the sum.
1. 16, 8, 4, …
2. 22, -44, 88, …