Arithmetic Sequence: Finding the Value of the First Term

This slide focuses on finding the value of the first term given any two values of an arithmetic progression.

1. ARITHMETIC SEQUENCE Finding the value of a 1 1 Solomon Hippocrates S. Flores E. Rodriguez Vocational High School

2. ANSWER TO Assignment 1. n = 46 2. d = 1 3. n = 72

3. Give the first three terms in the arithmetic sequence given the common difference . 1) a 1 = 2, d = 2

4. 2) a 1 = 2, d = -2

5. 3) a 1 = -11, d = 7

6. 4) a 1 = -3, d = -2

7. 5) a 1 = 24, d = -6

8. 6) a 1 = 36, d = -2

9. 7) a 1 = -1, d = 4

10. 8) a 1 = ½, d = 1

11. 9) a 1 = 8, d = - ½

12. 10) a 1 = 3x + 5, d = x - 2

13. Mario is a jeepney driver plying the route from Fairview to Quiapo . Every day he passes by the gasoline station to buy diesel gas for his jeepney . With the increasing prices of gasoline and diesel, he wants to monitor the number of liters of diesel he uses every day.

14. So, every day, he takes note of the number of liters of diesel his jeep uses up. It so happens that Mario lost his record. The only ones that he can remember is the amount used on Wednesday, his jeep used up 8 liters of diesel gas and on Saturday, it used up 9.5 liters of diesel gas. How many liters of diesel gas do you think will he buy at the start of the week {Monday) and everyday there after?

15. The above activity illustrates a sequence where the first term is missing while any two of the arithmetic progression is given. The general formula for the arithmetic sequence can be used to solve such situations.

16. Consider the following: 1. If the 3 rd term of an arithmetic sequence is 8 and the 16 th term is 47, find a 1 .

17. 2. Find the first term of the arithmetic sequence if a 12 = 47 and d = 3.

18. 3. If the 3 rd term in the arithmetic sequence is 2 and the 15 th term is -34. What is a 1 ? Give the next five terms.

19. Solve the following. , , 1. The 3 rd term of an arithmetic sequence is 8 and 7 th term is 20, find the first term. 2. Find the first term of the arithmetic sequence if a 100 = 702 and d = 7. 3. The 10 th and 12 th terms of an arithmetic sequence are 11 and 14, respectively. Find d and a 1 . 4. If the 6 th term of an arithmetic sequence is 27 and the 12 th term is 48, find the first term. 5. Find the first term of an arithmetic sequence whose 34 th term is -39 and 50 th term is -61.

20. VALUES INTEGRATION A sick child is given a dose of medicine every 8 hours. If the mother gave the first dose at 8am on Monday, how many times was the medicine given until Sunday evening? Write the sequence representing the time the mother gave the medicine to her sick child.

21. Solve the following. . , , 1. The 12 th term is -7 and the 25 th term is 6. Find a 1 . 2. The last term of the arithmetic sequence is 207, the common difference is 3 and the number of terms is 14. What is the first term? 3. What are the first four terms in the sequence if the third term is 4 and the fifth term is 20. 4. The 14 th term in an arithmetic sequence is 98 and the 15 th term is 105. Find a 1 . 5. If the 16 th term of an arithmetic sequence is 48 and the common difference is 3, find the first term.

22. Assignment , , 1. Find the first five terms in the arithmetic sequence given a 3 = 2 and a 5 = 10. 2. What are the first five terms of an arithmetic sequence whose 9 th term is 16 and 40 th term is 47? 3. Find the arithmetic sequence of 6 terms if the first term 2/3 is and the last term is 22/3.

23. Thank you!