MATH G10 SEQUENCES, different types, and solutions

Objectives:
a. Find the general term of a given
sequence.
b. Find few terms of the sequence
given the general term.

An activity to challenge the students to paraphrase and develop their comprehension skills.
Changing specific terms to general term.
Direction: Paraphrase the sentence or paragraph to change specific terms of items
or events to its general terms. Number 1 is given as an example
1. John bought some milk, bread, fruit,
cheese, potato chips, butter, hamburger
meat and buns.
Answer: John bought some groceries.

2. A lot of children came and brought presents. They
played games and blew bubbles at each other. A
magician came and showed them some magic. Later
Jennifer opened her presents and blew out the candles
on her cake.
3. George did the arithmetic problems. Then he did the
five-page reading assignment for social studies. Finally
he studied the spelling list for tomorrow's test.

2. A lot of children came and brought presents.
They played games and blew bubbles at each
other. A magician came and showed them some
magic. Later Jennifer opened her presents and
blew out the candles on her cake.
Answer: Jennifer had a birthday party.

3. George did the arithmetic problems.
Then he did the five-page reading
assignment for social studies. Finally he
studied the spelling list for tomorrow's
test.
Answer: George did his homework.

PRACTICING STUDENTS’ SKILLS IN FINDING THE NTH TERM OF A SEQUENCE.
a. What is the next term in the
given sequence 2,4,6,8,…?
b. What is the next three terms of
the sequence 5, 25, 45, 65,…?

a. What is the next term in the
given sequence 2,4,6,8,…?
Answer: 10

Answer: 85,105,125
b. What is the next three terms of
the sequence 5, 25, 45, 65,…?

Can you determine the 1000th term of
each given sequence?
1. 2,4,6,8,…
2. 5,25,45,65,…

2,4,6,8,…
If it increases moderately, think about multiples of the term
number plus or minus a constant like: 2n or 3n – 1.
𝑎𝑛 = 2𝑛
𝑎1 = 2 1 = 2 𝑎2 = 2 2 = 4
𝑎3 = 2 3 = 6 𝑎4 = 2 4 = 8

2,4,6,8,…
4 − 2 = 2
6 − 4 = 2
8 − 6 = 2
𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2
𝑎𝑛 = 2𝑛

Determine the 1000th term of the sequence 2,4,6,8,…
𝑛 = 1000
𝑎𝑛 = 2𝑛
𝑎𝑛 = 2𝑛
𝑎1000 = 2(1000)
𝑎1000 = 2000

Determine the 1000th term of the sequence 5,25,45,65,…
25 − 5 = 20 45 − 25=20 65 − 45 = 20
𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 20
𝑎1 = 20𝑛 − 𝑐 = 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 = 5 𝑎𝑛 = 20𝑛 − 15
𝑎1 = 20 1 − 15 = 20 − 15 = 5
𝑎2 = 20 2 − 15 = 40 − 15 = 25
𝑎3 = 20 3 − 15 = 60 − 15 = 45
𝑎4 = 20 4 − 15 = 80 − 15 = 65
𝑎1000 = 20 1000 − 15 = 20000 − 15 = 19985

PRACTICING STUDENTS’ SKILLS IN FINDING THE FIRST FOUR TERMS OF A SEQUENCE.
Write the first four elements of the
sequence whose general term is given.
1. an=3n
2. an=2n-1
3. an=n+4

1. an=3n
n = 1,2,3,4 a1=3(1) = 3
a2=3(2) = 6
a3=3(3) = 9
a4=3(4) = 12
3,6,9,12

2. an=2n-1
3. an=n+4

2. an=2n-1 n = 1,2,3,4
a1=2(1)-1 = 2-1 = 1
a2=2(2)-1 = 4-1 = 3
a3=2(3)-1 = 6-1 = 5
a4=2(4)-1 = 8-1 = 7
1,3,5,7

3. an=n+4 n = 1,2,3,4
a1=1+4=5
a2=2+4=6
a3=3+4=7
a4=4+4=8
5,6,7,8

Create your own
example of
sequence and give
its general term.

Solve:
1. Lara deposited Php.20,000 on an investment that will give
Php.1,750 for every year that her money stays in the
account. (a) Write the nth term or the general term. (b)How
much money will she have in her account by the end of year
8?
Answer: a. an = Php.20,000+(n-1) Php.1,750
b.Php.32250

I.Find the nth term or the general term of each sequence.
1.1,4,7,10,…
2. 5,9,13,17,21,…
II.Find the first three terms of the sequence defined by each
equation.
1.tn = 5-n2
2. tn = 50 – 5n

I.Find the nth term or the general term of each sequence.
1.1,4,7,10,…
Answer: 3n-2
2. 5,9,13,17,21,…
Answer: 4n+1
II.Find the first three terms of the sequence defined by each equation.
1.tn = 5-n2
Answer: {4,1,-4}
2. tn = 50 – 5n
Answer: {45,40,35}

MATH G10 SEQUENCES, different types, and solutions

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