powerpoint presentation

1. Ms. G. Martin

2. • A geometric sequence is a sequence such that each
term is obtained by multiplying the preceding term by
a constant.
• To find the nth term of a geometric sequence, use the
formula Xn = X1rn-1 where r is the constant multiplier,
which is known as the common ratio.
• The common ratio is obtained by using the formula r
=
Xn
Xn−1

3. Let’s Learn!
Kristine saves Php 20 from her monthly allowance on the first month, Php
on the second month, Php 80 on the third month, Php 160 on the fourth
month. If she will save continuously in this manner, how much will she
save on the tenth month?
Let us tabulate Kristine’s monthly savings for the first ten months.
Month 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
Amount of
savings
Php20 Php40 Php80 Php160 _____ _____ _____ ____ ____ ____

4. Observe the following cases.
Php 20(2) = Php40 Php 80(2)= Php160 Php 320(2) = Php640
Php 40(2) = Php80 Php160(2) = Php320 Php 640(2) = Php1,240
The sequence {20, 40, 160,…} illustrate a geometric sequence.
Notice that the sequence has a constant multiplier 2 in obtaining the
second term, third term,…nth term.
In general, the terms of a geometric sequence can be represented as follows:
1st term: A1
2nd term : A2 = A1r
3rd term: A3 = A2r
4th term: A4 = A3r
5th term: A5 = A4r

5. Example 1. What is the 10th term of the geometric
sequence 2, 6, 18, 54, 162, …?
Solution:
rn =
An
An−1
rn =
6
2
r = 3
Solving for the 1oth term,
An = A1rn-1
A10 = (2)(310-1)
A10 = (2)(39)
A10 = (2)(19,683)
A10 = 39,366

6. Example 2. Find the 14th term of the geometric sequence
8, 4, 2, 1, …
Steps Solution
1 Identify the given information A1 = 8, A2, = 4 and n = 14
2. Find the common ratio. r =
A2
A1
=
4
8
=
1
2
3. Solve for the 14th term of the
geometric sequence using the
formula An = A1rn-1 .
A14 = A1r14-1 = 8(
1
2
)13
= 8(
113
213 ) = 8(
1
8,192
) =
8
8,192
A14 =
1
1,024

7. Thank You!
SMSDGRADE10-MT.
TRIUMPH@ODL2020