lesson

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Study & complete the following sequences.
1. 8, 14, 20, 26, _______
2. 9, 13, 17, 21, _______
3. 5, 15, 45, __________
4. 999, 333, 111, ______
5. 18, 14, 10, _________
Find me!

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Consider the picture at below:
1. Do you see any pattern form the
given picture?
2. Write the terms of coffee bean.
2. If the pattern continues what will
be next term?
3. Can you give an equation that
will satisfy the sequence form by
the coffee bean?

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SLIDESMANIA.COM
Identify the First Few Terms of a
Sequence given the nth Term of a
Sequence
Republic of the Philippines
D E P A R T M E N T O F E D U C A T I O N
REGION VI-WESTERN VISAYAS
SCHOOLS DIVISION OF CAPIZ
CAPIZ NATIONAL HIGH SCHOOL

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SLIDESMANIA.COM
How do you generate a sequence
from a given rule/nth term?

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SLIDESMANIA.COM
The terms in a sequence can be written as
a1, a2, a3,…
Which means;
a1 is the first term
a2 is the second term
a3 is the third term
an is the nth term of the sequence.
• This is called the general term or nth term.

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SLIDESMANIA.COM
Sometimes a pattern in the sequence can
be obtained and the sequence can be
written using a general term.

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EXAMPLE:
Given an = n + 2, list the first 4 terms of the
sequence.
Solution:
To find the first term, let n = 1
an = n + 2 use the given generated term
a1 = 1 + 2 substitute n by 1
a1 = 3 perform the operations
simplify

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To find the 2nd term, let n = 2
an = n + 2
a2 = 2 + 2
a2 = 4
To find the 3rd term, let n = 3
an = n + 2
a3 = 3 + 2
a3 = 5

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To find the 4th term, let n = 4
an = n + 2
a4 = 4 + 2
a4 = 6
Therefore, the first four terms of the sequence
are 3, 4, 5, 6.

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EXAMPLE:
Given an = 2n-1, list the first 4 terms of the sequence.
Solution:
To find the first term, let n = 1
a1 = 2n-1 use the given generated term
a1 = 2(1)-1 substitute n by 1
a1 = 2 – 1 perform the operations
a1 = 1 simplify

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Repeat the same process for the second to the
fourth terms.
Find the 2nd term, n=2
a2 = 2n-1 use the given generated term
a2 = 2(2)-1 substitute n by 2
a2 = 4 – 1 perform the operations
a2 = 3 simplify

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Repeat the same process for the second to the
fourth terms.
Find the 3rd term, n=3
a3 = 2n-1
a3 = 2(3)-1
a3 = 6 – 1
a3 = 5

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Repeat the same process for the second to the
fourth terms.
Find the 4th term, n=4
a4 = 2n-1
a4 = 2(4)-1
a4 = 8 – 1
a4 = 7
Therefore, the first four terms of the sequence are
1,3,5,7.

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Let’s answer the following exercises.
1. Find the first 5 terms of the sequence
an = n +3
2. Find the first 5 terms of the sequence
an = n +5