Mathematics 10 Quarter 1 : Arithmetic Sequence
- 1. z ARITHMETIC SEQUENCE MATH 10 – TOPIC #2
- 2. z  In the previous lesson, you have learned that a sequence is an arrangement of objects, numbers or even figures which follows a certain pattern. Also, you have learned about the processes in finding patterns of any sequence. Look at the sequences below. Can you see the specific pattern they follow 2, 4, 6, 8, … 3, 6, 12, 24, … 5, 10, 15, 20, …
- 3. z Observe the following sequences:  1. 4, 7, 10, 13, …  2. 33, 38, 43, 48, …  3. -2, -6, -10, -14, …  4. 100, 98, 96, 94, …  5. 1/2 , 1, 1 1/2, 2, …
- 4. z Arithmetic Sequences A sequence in which term after the first is formed by adding a fixed number to the preceding term is called arithmetic sequence. The fixed number or constant is called the common difference denoted by 𝒅
- 5. z 1. Determine if the sequence is arithmetic or not. If it is, find the common difference and the next three terms of the sequence. -4, 3, 10, 17, …
- 6. z  2. Write the first five terms of the arithmetic sequence with 5 as the first term and with a common difference of -2.
- 7. z 3.Find the common difference in an arithmetic sequence whose 𝑎2 = 1, 𝑎5 = 7.
- 8. z 4. Find the common difference of the arithmetic sequence 3a -1, 3a, 3a + 1, …
- 9. z 5. Find the value of a to make 3a +1, 4a, 6a + 1, … an arithmetic sequence?
- 10. z  6. I was advised by my physician to walk each day in the morning as a daily exercise. On the first day, I walked 40m. On the second and third day, I walked 60m and 80m, respectively, and so on. Which of the following is the distance I walked on the 10th day if I continue the pattern in my daily walk?
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- 12. z Let us investigate on how to determine the nth term of a sequence.  a1 = 3 + 0 = 3  a2 = 3 + 5 = 8  a3 = 3 + 5 + 5 = 13  a4 = 3 + 5 + 5 + 5 = 18 3, 8, 13, 18, …
- 13. z The nth term of an arithmetic sequence with first term a1 and common difference d is given by: an = a1 + d (n-1)
- 14. z A.Find the 21st term of the arithmetic sequence: 6, 9, 12, 15, … Let us apply the formula in solving the following problems:
- 15. z B. In the arithmetic sequence: 7, 10, 13, 16, . . .; find n if an = 304. Let us apply the formula in solving the following problems:
- 16. z C. The 3rd term of an arithmetic sequence is 8 and the 16th term is 47. Find d, 𝑎1 and the 71st term. Let us apply the formula in solving the following problems:
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