Recall the different formulas used for the
different kinds of sequences;
Soving problems involving
different types of sequences;
Demonstrate appreciation on the application
of sequences in real-life situations.
Objective
s
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Sequences are used in various fields to model, analyze, and solve problems involving ordered lists of numbers or objects that follow specific patterns.
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Recall the different formulas used for the
different kinds of sequences;
Soving problems involving
different types of sequences;
Demonstrate appreciation on the application
of sequences in real-life situations.
Objective
s
Activity 1: REVIEW
Recall the different
formulas used for the
different kinds of
sequences
SEQUENCE
It is an ordered list of
numbers.
GEOMETRIC SEQUENCE
It is a sequence where each term after
the first is obtained by multiplying the
preceding term by a fixed number.
The common difference (d)
can be determined by
SUBTRACTING any term in
the sequence by the terms
that precedes it.
How do we obtain the d in an
arithmetic sequence?
The next term can be
determined by ADDING a
constant called a common
difference.
How do we obtain the next term in an
Arithmetic Sequence?
The next term can be
determined by MULTIPLYING
the preceding term by a
fixed number called a
common ratio.
How do we obtain the next term in a
Geometric Sequence?
What is the general rule in finding the
nth term of an arithmetic sequence?
๐
๐
- ( ๐ โ ๐ ) ๐
What are the formula for finding the
sum of the terms of an arithmetic
sequence?
๐บ ๐
=
๐
๐
( ๐จ ๐ +^ ๐จ๐ )
๐บ ๐
=
๐
๐
[ ๐ ๐จ ๐
+(^ ๐ โ ๐ )^ ๐ ]
or
What are the formula for finding the
sum of the terms of a geometric
sequence?
or
๐บ ๐
=
๐จ ๐
( ๐ โ ๐
๐ )
๐ โ ๐
๐บ ๐
=
๐จ ๐
๐ โ ๐
To solve problems involving
sequences:
- Determine the type of sequence involve
in the
problem.
- Use the appropriate formula.
- Perform the indicated operations and simplify
To replace the trees destroyed by typhoon Yolanda, the Department
of Environment and Natural Resources has developed a ten-year
plan. The first year they will plant 300 trees. Each succeeding year,
they will plant 50 more trees than they planted the year before.
How many trees will they have planted by the end of the 10
th year?
1 2 3 4 5 6 7
8 9 10
Given:
1
๐ =ยฟ
๐ =ยฟ
๐
๐บ ๐
=
๐
๐
[ ๐ ๐จ ๐
+(^ ๐ โ ๐ )^ ๐ ]
๐ 10
=
10
2
[ 2 ( 3 00 )+(^10 โ 1 )^50 ]
๐ 10
= 5 [ 6 00 +( 9 ) 50 ]
10
10
๐๐
Thus, there are
5,250 trees planted
at the end of 10
th
year.
3 00
50
10
A ball tossed to a height of 8 meters rebounds to its
previous height. What is the total distance the ball has
travelled until it comes to rest.
Note: The distance travelled going up is the same
as the distance travelled going down.