Sequence and Series TI-83 Lab

Sequence and Series – TI-83 lab

Definition: If the function u(n) or un represents an arithmetic sequence with common difference d and first term u(1) or u1 , then the sum of the first n terms of the sequence is represented by: S(n)  u(1)  u(2)  u(3)  ...  u(n)or Sn  u1  u2  ...  un

n S  2u  n 1d  This sum can be found by using the formula: n 2 1

Given un = 7n-3

1. Write the first 8 terms.

2. Use a calculator to add the first 8 terms. The sum is

represented by S8 . S8 = ______.

3. Use the formula described above to find S8 . Show your work.

4. Use the formula to find the sum of the first 500 terms, 700 terms and 999 terms. The TI-83 can add the terms of the sequence using the sum seq command.

5. Use the sum seq command on your calculator to find S8 . 8 S Mathematically we represent 8 as 7n  3 . K 1

To enter this on your TI-83(Buttons are in bold):  Press 2nd STAT to access the LIST menu  Use arrow to select the MATH menu.  Type 5 to select sum(  Press 2nd STAT to access the LIST menu  Use arrow to select OPS menu  Type 5 to select seq(  Type 7K-3, K, 1, 8, 1)) followed by ENTER  sum(seq(7K-3, K, 1, 8, 1))  7K-3 is the sequence, K is the variable being change, 1 and 8 are the beginning and end respectively and the second 1 is the count.

6. Use the sum(seq( to find S95 , S150 , and the S50 .

Definition: If the function un represents a geometric sequence with common ratio r and first term u1 then the sum of the first n terms of the sequence is represented by: Sn  u1  u2  ...  un .

n Mathematically S n = uk K 1 u 1 r n  This sum can be found by using the formula: S  1 n 1 r

n Given the sequence un = 2(1.1)

7. Find the first 6 terms.

8. Use a calculator to add the first 6 terms. This sum is S6 .

9. Use the formula above to find S6 . Show your work.

10. Use the formula to find the sum of the first 500 terms, 700 terms and 999 terms.

11. Use the sum(seq( to find S95 , S150 , and the S50 .

Application You receive two job offers. The first pays $3000 for the first month and a $100 more each month. The second pays $500 for the first month and 10% more each month.

12. Write a formula for each job using sum notation.

13. What is the total amount earned from job 1 after two years(24 months)?

14. What is the total amount earned from job 2 after two years(24 months)?

15. Which job offer should you accept and why?