Sequence and Series – TI-83 lab



Sequence and Series – TI-83 lab

Definition: If the function u(n) or [pic] represents an arithmetic sequence with common difference d and first term u(1) or [pic], then the sum of the first n terms of the sequence is represented by:[pic]

This sum can be found by using the formula: [pic]

Given [pic] = 7n-3

1. Write the first 8 terms.

2. Use a calculator to add the first 8 terms. The sum is represented by [pic]. [pic] = ________.

3. Use the formula described above to find [pic]. 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 [pic]. Mathematically we represent [pic] as [pic].

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 [pic], [pic], and the [pic].

Definition: If the function [pic] represents a geometric sequence with common ratio r and first term [pic] then the sum of the first n terms of the sequence is represented by: [pic].

Mathematically [pic] = [pic]

This sum can be found by using the formula: [pic]

Given the sequence [pic] = [pic]

7. Find the first 6 terms.

8. Use a calculator to add the first 6 terms. This sum is [pic].

9. Use the formula above to find [pic]. 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 [pic], [pic], and the [pic].

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?

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