OBJECTIVE
• We will find the missing
terms in an arithmetic and a
geometric sequence by
looking for a pattern and
using the formula.
Use the formula to find the nth
term in an arithmetic sequence.
An= A1 + (n-1)d
1. 25th term in the sequence 3,
7, 11, 15, 19 …
Use the formula to find the nth
term in an arithmetic sequence.
An= A1 + (n-1)d
nd
62 ,
th,
200
th
20
2. Find the
term
in the sequence 3, 7, 11, 15, 19
…
Use the formula to find the nth
term in an arithmetic sequence.
An= A1 + (n-1)d
3. What is the 47th term in the
sequence?
21, 15, 9, 3, . . .
Use the formula to find the nth
term in an arithmetic sequence.
An= A1 + (n-1)d
4. What is the 80th term in the
sequence?
21, 15, 9, 3, . . .
ARITHMETIC
SEQUENCE
-is a numerical pattern with
a common difference.
- have an addition or
subtraction rule.
• Vocabulary
• Sequence- a set of numbers
{1, 3, 5, 7, …}
• Terms- each number in a sequence
• Common Difference- the number
added to find the next term of an
arithmetic sequence.
3, 7, 11, 15, 19 …
What is the common difference?
+4
What is the seventh term in the
sequence?
3, 7, 11, 15, 19 , 23, 27
To find the next term…
look at the PATTERN for the
preceding terms
Ex. 1, 5, 9, ___, ____
Pattern: Add 4
FIND the 5th term in the sequence
-28, -17, -6, 5…
1. Find the common difference by
subtracting the 2nd term and the
1st term: +11
2. Add 11 to the 4th term in the
sequence:
5 + 11= 16
ANSWER: The 5th term is 16
FIND the 10th term in the sequence
-28, -17, -6, 5…
1. Find the common difference by
subtracting the 2nd term and the 1st
term: +11
2. Add 11 from the 4th to the 10th term
in the sequence:
-28, -17, -6, 5, 16, 27, 38, 49, 60, 71
ANSWER: The 10th term is 71
GEOMETRIC SEQUENCE
–The ratio of successive
terms in a geometric
sequence is a constant
called the common ratio,
denoted by r.
Find the common ratio and
the 8th term of the
following:
1) 1, 2, 4, 8, 16, ...
2) 27, 9, 3, 1, 1/3, ...
3) 3, 6, 12, 24, 48, ...
4) 1/2, -1, 2, -4, 8, ...
This is important!
Arithmetic formula:
an = a1 + (n - 1)d
an is the nth term, a1 is the first term, and
d is the common difference.
Geometric formula:
an = a1 . r (n - 1)
an is the nth term, a1 is the first term, and r
is the common ratio.
Let's play guess the sequence!: I give you a
sequence and you guess the type.
1. 3, 8, 13, 18, 23, . . .
2. 1, 2, 4, 8, 16, . . .
3. 24, 12, 6, 3, 3/2, 3/4, . . .
4. 55, 51, 47, 43, 39, 35, . . .
5. 2, 5, 10, 17, . . .
6. 1, 4, 9, 16, 25, 36, . . .
Answers!
1) Arithmetic, the common difference d = 5
2) Geometric, the common ratio r = 2
3) Geometric, r = 1/2
4) Arithmetic, d = -4
5) Neither, why? (How about no common
difference or ratio!)
6) Neither again! (This looks familiar, could it
be from geometry?)
Sample problems:
Find the first four terms and state whether the sequence is
arithmetic, geometric, or neither.
1) an = 3n + 2
2) an = n2 + 1
3) an = 3*2n