10
Department of Education-Region III
TARLAC CITY SCHOOLS DIVISION
Juan Luna St., Sto. Cristo, Tarlac City 2300
Email address: [email protected]/ Tel. No. (045) 470 - 8180
MATHEMATICS
Quarter 1: Week 1
Learning Activity Sheet
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Department of Education-Region III
TARLAC CITY SCHOOLS DIVISION
Juan Luna St., Sto. Cristo, Tarlac City 2300 Email address: [email protected]/ Tel. No. (045) 470 - 8180
MATHEMATICS
Quarter 1: Week 1
Learning Activity Sheet
MATHEMATICS 10
Name: Date: Section: Quarter 1 - Week 1
Generating Patterns and Illustrating Arithmetic Sequence
Brief Introduction:
Recognizing and extending patterns are important skills needed for learning concepts related to Sequence. Given at least the first 3 terms of a sequence you can easily find the next term in that sequence by simply discovering a pattern as to how the third term is derived from the second term, and the second term from the first term. You will find that either a constant number is added, subtracted, multiplied, or divided to get the next term or a certain series of operations is performed to get the next term.
The nth term that generates the pattern of a sequence Examples:
- Find the nth term that generates the pattern for the sequence 2, 8, 18, 32, โฆ
Solving a problem like this involve some guessing. Looking over the first 4 terms, see that each is twice a perfect square:
Answer: The nth term for the sequence 2, 8, 18, 32, โฆ is an = 2n^2.
- Find the nth term that generates the pattern for the sequence 2,
3 8
4
5 64
Answer: The nth term for the sequence ๐,
๐ ๐
๐
๐ ๐๐ , โฆ is ๐๐ =
๐๐^
๐ 1 = 2 = 2 ( 1 ) = 2 ( 1 )^2
๐ 2 = 8 = 2 ( 4 ) = 2 ( 2 )^2
๐ 3 = 18 = 2 ( 9 ) = 2 ( 3 )^2
๐ 4 = 32 = 2 ( 16 ) = 2 ( 4 )^2
๐๐ = 2 ๐^2
๐^3
Arithmetic sequence is a sequence where each term after the first is obtained by adding the same constant called the common difference (d).
Common difference (d) 4 4 4 4 4
Determine whether the given sequence is an arithmetic sequence or not.
Sequences Arithmetic Sequence or Not Pattern
- 3, 9, 15, 21, โฆ Arithmetic Sequence Adding 6
- 2, 6, 18, 54, โฆ Not an Arithmetic Sequence Multiplying by 3
- 120, 60, 30, 15, โฆ Not an Arithmetic Sequence Multiplying by ยฝ
- 22, 17, 12, 7, โฆ Arithmetic Sequence Adding -
- -2, 2, -2, 2, โฆ Not an Arithmetic Sequence Multiplying by -
Common difference of an Arithmetic Sequence
Arithmetic Sequences
First Term
Second Term
Common Difference (d)
First five terms of an Arithmetic Sequence
Examples:
Determine the first term by substituting 1 to n.
1 st^ term a 1 = 7(1) โ 1 = 7 โ 1 = 6 2 nd^ term a 2 = 7(2) โ 1 = 14 โ 1 = 13 3 rd^ term a 3 = 7(3) โ 1 = 21 โ 1 = 20 4 th^ term a 4 = 7(4) โ 1 = 28 โ 1 = 27 5 th^ term a 5 = 7(5) โ 1 = 35 โ 1 = 34
Another solution: The coefficient of n in an = 7n โ 1 is 7, therefore, the common difference is 7.
6, (6 + 7), (13 + 7), (20 + 7), (27 + 7) 6, 13, 20, 27, 34
Answer: The first five terms of the arithmetic sequence an = 7n โ 1 are 6, 13, 20, 27, 34.
1 st^ term a 1 = -5(1) + 3 = -5 + 3 = - 2 2 nd^ term a 2 = -5(2) + 3 = -10 + 3 = - 7 3 rd^ term a 3 = -5(3) + 3 = -15 + 3 = - 12 4 th^ term a 4 = -5(4) + 3 = -20 + 3 = - 17 5 th^ term a 5 = -5(5) + 3 = -25 + 3 = - 22
Another solution: The coefficient of n in an = -5n + 3 is -5, therefore, the common difference is -5.
-2, (-2 + (-5)), (-7 + (-5)), (-12 + (-5)), (-17 + (-5))
- 2, - 7, - 12, - 17, - 22
Answer: The first five terms of the arithmetic sequence an = -5n + 3 are -2, -7, -12, - 17, -22.
- ๐๐ =
๐ ๐ ๐ โ ๐
1 st^ term ๐๐ =
๐ ๐
(๐) โ ๐ = ๐ โ ๐ ๐ =
๐ ๐
2 nd^ term ๐๐ = ๐ ๐ (๐) โ ๐ = ๐ โ ๐ ๐ = ๐ ๐ = ๐
3 rd^ term ๐๐ =
๐ ๐ (๐) โ ๐ = ๐ โ ๐ ๐ =^
๐ ๐
4 th^ term ๐๐ =
๐ ๐
(๐) โ ๐ = ๐๐ โ ๐ ๐ =
๐๐ ๐ = ๐
5 th^ term ๐๐ =
๐ ๐ (๐) โ ๐ = ๐๐ โ ๐ ๐ =^
๐๐ ๐
Activity 3 Determine the common difference (d) in each of the following Arithmetic sequence.
- 8, 14, 20, 26
- 17, 15, 13, 11
- -7, -1, 5, 11
- 11, 12, 13, 14
- 4, 14, 24, 34
Activity 4 Determine the common difference and fifth term of the following arithmetic sequence. Provide complete solution in each item.
Arithmetic Sequence Common Difference Fifth Term
Activity 5 Determine the corresponding nth term that generates the pattern of the following sequences. Provide complete solution in each item.
Reflection Give at least two examples of real-life objects that show a specific pattern. Describe how each object looks.
Reference
Deseree G. Ofiaza. Brainworks: A Skill Book for K to 12 Mathematics 10, Makati City: Diwa Learning System, Inc. 2015. 5
Melvin M.Callanta, et.al. Mathematics Grade10 Learnerโs Module, Pasig: Department of Education, 2015, 9 - 13.
Answers Key
Activity 1
1. B
2. B
3. A
4. B
5. C
Activity 2
1. NAS
2. AS
3. AS
4. NAS
5. AS
Activity 3
Prepared by:
CRISTINA S. BERCHES
Master Teacher II