Vocab & Terms
A set of numbers arranged in particular terms
What is sequence
A geometric sequence, starting with 1, with a 1:4 ratio. (5 terms)
What is 1, 4, 16, 64, 256
An arithmetic sequence, starting with 6.01, with a common difference of .25. (5 terms)
What is 6.01, 6.26, 6.51, 6.76, 7.01
A sequence, beginning with 5, with a ratio of 1:6. Identify the type. (5 terms)
5, 30, 180, 1080, 6480
Geometric
On January 1st Komi puts $100 into his bank account. On the first of each month after that he deposits an additional $10.
How much money is in Komi's account at the end of February?
$110
The number of terms you wish to find in the sequence.
A geometric sequence, starting at 5, with a 1:3 ratio. (5 terms)
What is 5, 15, 45, 135, 405
An arithmetic sequence, starting with 89, with a common difference of two. (5 terms, decreasing)
What is 89, 87, 85, 83, 81
An sequence, beginning with -7, with a common difference of 3. Identify the type.
( 6 terms, decreasing)
-7, -10, -13, -16, -19, -22
Arithmetic
John has purchased 20 books. The 1st book cost $1, the 2nd, $2, the 3rd, $4, and the 4th ,$8, and so on. How much did John pay for the 20 books?
$1,048,575
The common ratio
What is r
A geometric sequence, starting with 3, with a ratio of 1:5. (5 terms)
What is 3, 15, 75, 375, 1875
Arithmetic sequence, beginning with -12, with a common difference of 10. (6 terms)
What is -12, -2, 8, 18, 28, 38
The sixth term in the sequence, beginning with 3, with a ratio of 1:2.
3, 6, 12, 24, 48, 96
Mo reads a lot of books. When he was five years old he read 4 books. Each year he reads three more than twice the number of books he read the previous year.
How many books does Mo read when he's six years old?
11
A sequence with a common difference between terms
What is arithmetic sequence
The explicit rule of the geometric sequence with a1=4 & a4=4/27.
What is 4(1/3)n-1
An arithmetic sequence, beginning with 45, with a common difference of 4. (7 terms)
45, 49, 53, 57, 61, 65, 69
The second term of a geometric sequence is 6, and the fifth term is 48. Determine the sequence.
3, 6, 12, 24, 48
In 2013, the number of students in a small school is 284. It is estimated that the student population will increase by 4% each year.
1.The formula for the student population.
2.The population in 2020
1. an= (284)(1.04)n
2. 374
Sequence with a ratio between consecutive terms
What is geometric sequence
Find the 18th term of a geometric sequence with a first term of 5 and a common ratio of 3.
What is 645,700,815
The arithmetic sequence formula
an= a1+(n-1)d
The two equations for the sequence with terms
a5= −32 and a18= 85
a5= -32: -32=a1+4d
a18= 85: 85=a1+17d
Mike deposited $850 into the bank in July. From July to December, the amount of money he deposited into the bank increase by 25% per month. What’s the total amount of money in his account after December? Round your answer to the nearest dollars
$9570