Part 1

Patterns and Sequences

2

FINITE OR INFINITE

1,2,3,4,5,...

INFINITE

4

Is this a pattern or a set

7, 1, 0, 3, 4, 2, 5

Set---order doesn't matter, and there are no repetitions in the numbers.

6

True or False

A Sequence is a set of terms in which each term can only repeat once.

False---Set

10

What do you call the first term and the last term of a sequence?

Extremes

15

Sequence is an enumerated collection of objects in which repetitions are allowed and _____, and follows a particular ____/ ____

Order matter, rule/pattern

General Term

2

2, 3, 4, 5, 6

a_n=n+1

4

What are the first 5 terms of:

6n+7

13, 19, 25, 31, 37

6

What is the general term in:

3, 6, 11, 18, 27

a_n=n²+2

10

What is a general term in the sequence:

1/2, 1/5, 1/10, 1/17, 1/26

a_n=1/(n²+1)

15

What is the general term in:

10, 15, 27, 50

NONE

Finite Series

2

What is the sum of the sequence:

1,3,5,7,9

25

4

Identify the parts:

(1.)

Σ (2.)

n=(3.)

1. Upper limit

2. General Term

3. Index/ Lower Limit

6

Write the sigma notation of the given sequence (n=1):

1,8,27,64

4 

Σ (n³)

n=1

10

What is the sum of this summation (hint: what does a sigma notation have to have):

5
Σ 2n+1

n=1

None, since there is no parenthesis in the general term.

15

Find the sum:

8

Σ [n(n+1)/2]

n=3

116

Arithmetic

2

True or False: 

In the sequence 1, 4, 7, 10, the r is 3 

FALSE---d=3 not r

4

Find the 67th term of 2, 4, 6, 8, 10

a₆₇=134

6

The 6th term of a sequence is 69, and the 9th term of a sequence is 420. What formula could make this sequence?

a_n=117n-633

10

Albert is at 67m as his initial position, he travels to 134m in the first minute, and 201m in the 2nd minute. At what distance will he be at the 5th minute?

402m

15

Find the value of x that would make this an arithmetic sequence?

6x+7, 2x-7, 6x-9

x= -3/2

Arithmetic Series

2

Find the sum of the first 50 counting numbers.

1275

4

What is the d where the 3th term is 67 and the 5th term is 101?

d=17

6

Find the sum of the first 10 terms of the sequence 3,10,17,24

S₁₀=345

10

Albert saves money for a vacation by depositing $50 in the first month, $70 in the second month, $90 in the third month, and increases his savings by $20 each month. How much will Tom have saved after 12 months?

$1920

15

Find the sum of all the even integers from -1000 to 6700

10975350