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
This sum can be found by using the formula: S n  2u1  n  1d 
n
2
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
Mathematically we represent S8 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 S 95 , S150 , and the S 50 .
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 =
u
K 1
k

u1 1  r n
This sum can be found by using the formula: S n 
1 r
Given the sequence un =

2(1.1) n
7. Find the first 6 terms.
8. Use a calculator to add the first 6 terms. This sum is S 6 .
9. Use the formula above to find S 6 . 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 S 95 , S150 , and the S 50 .
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?