Reviewer in Math 10 – First Quarter
The terms between any two nonconsecutive terms
of an arithmetic sequence are known as
Arithmetic Means.
The sum of the terms of an arithmetic sequence is
called arithmetic series.
PATTERN AND SEQUENCE
Pattern is a set of elements repeated in a
predictable manner.
(For Arithmetic Series)
Sequence does not need to have a pattern.
Pattern is not well defined, while sequence is a
well-defined mathematical terms, geometric
shapes or other objects, that follow a specific
pattern.
Sequence - is an ordered list of numbers (or
other elements like geometric objects), that often
follow a specific pattern or function.
GEOMETRIC SEQUENCE
A sequence in which each term is obtained by
multiplying the preceding term by a fixed
number (r) is a Geometric Sequence.
r = a2 ÷ a1 (Finding r)
an = a1rn-1 (General Formula)
The terms between any two nonconsecutive
terms of a geometric sequence are called as
Geometric Means.
Example of Sequence:
2; 4; 6; 8; ...
2 is the 1st term
4 is the 2nd term
6 is the 3rd term
8 is the 4th term
...(ellipsis) (three dots) meaning that the
sequence continues forever.
m1 = (To find the middle term)
The sum of the terms of a geometric sequence is
called Geometric Series.
(When no last term)
Sequences can be both finite and infinite.
Terms are the individual elements in a sequence.
Infinite or Finite - When the sequence goes on
forever it is called an infinite sequence,
otherwise it is a finite sequence.
EXPLICIT AND RECURSIVE FORMULA
FOR A SEQUENCE
Explicit formula for a Sequence
- Allows us to find the value of any term in the
sequence.
Recursive Formula for a Sequence
- Allows us to find the value of the nth term in
the sequence if we know the value of the (a-1)th
term in the sequence.
ARITHMETIC SEQUENCE
(When there is last term)
HARMONIC SEQUENCE
A Harmonic sequence is a set of fractions that
have pattern just like from Arithmetic Sequence,
but the difference is that we first need to find the
reciprocal of the terms before we subtract them
with there previous terms.
For Example:
The constant (d) is called the Common
Difference.
A sequence whose consecutive terms have a
common difference (d) is an Arithmetic
sequence.
d = a2 – a1 (Finding d)
an = a1 +(n-1)d (General Formula)
1.)
Step 1: Reciprocals.
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Reviewer in Math 10 – First Quarter
Step 2: Know if arithmetic.
8–6=2
6–4=2
4–2=2
Therefore, the sequence is harmonic.
Any term between two given terms of a
harmonic sequence is called harmonic mean.
The sum of the terms in a harmonic sequence is
called harmonic series.
FIBONNACI SEQUENCE
It is the continuous addition of previous
numbers.
For example:
a1 = 1
a2 = a1 = 1
a3 = a2 + a1 = 1 + 1 = 2
a4 = a3 + a2 = 2 + 1 = 3
a5 = a4 + a3 = 3 + 2 = 5
and so on…
SYNTHETIC DIVISION
LONG DIVISION
For example:
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