Patterns and Recognition
What is the pattern in this sequence?
5, 1, 1/5, 1/25, …
divide by 5
Find a50 of this arithmetic sequence:
-24, -20, -16, …
172
The formula for a Geometric sequence
An=A1(r)(n-1)
Find the common difference or ratio to find the next term of the sequence:
-1, -2, -4, -8, __
r= 2
A5= -16
Find the common difference or ratio to find the next 2 terms in the sequence
0, -4, -8, -12,__, __,...
d= -4
A5= -16
A6= -20
The pattern of a sequence is “multiply by 2 and then add 3”. If the first term of this sequence is -4, what are the next two terms?
-5 and -7
Write the explicit formula for this sequence:
-24, -20, -16, …
an=4n-28
What is the common ratio in this sequence?
1, 2, 4, 8, 16, 32...
r=2
Arithmetic, geometric, or neither?
22, 44, 66, 88...
Arithmetic
d= 22
Find the 10th term:
53, 50, 47, 44, 41...
A10= (53)+(10-1)(-3)
A10=26
Is this sequence arithmetic? geometric? or neither?
4, -2, -14, -38, …
neither
How many terms are in this sequence?
1, 3, 5, 7,…, 43
22 or 22 terms
Arithmetic, geometric, or neither?
-10, -30, -50, -70...
Arithmetic
d= -20
Arithmetic, geometric, or neither?
-0.5, 1, -2, 4,...
Geometric
r= -2
What does "r" stand for in an arithmetic sequence equation?
Nothing- "r", or common ratio, is not a part of Arithmetic sequences
Find the common ratio.
-2/3, -5/6, -25/24, …
5/4
Find the 30th term:
11, 20, 29, 38...
A30= (11)+(30-1)(9)
A30= 272
Find the sum of the first 10 terms of the following sequence:
3, 15, 75, …
7,324,218
Arithmetic, geometric, or neither?
4, 8, 16, 32,...
Geometric
r= 2
Find the first and fourth terms
__, 20, 29, __, 47,...
d= 9
A1= 11
A4= 38
What is the common difference in this sequence?
31, -69, -169, -269
d= -100
Find the sum of this series:
8.9+17.8+26.7+35.6+44.5+…+1619.8
148,211.7
Find the first and fifth terms
__, 10, -50, 250, __,...
r= -5
A1= -2
A5= -1,250
Find the first and fourth terms
__, 20, 29, __, 47,...
d= 9
A1= 11
A4= 38
Find the common difference or ratio to find the next term of the sequence:
-1, -2, -4, -8, __
r= 2
A5= -16