Examples with solutions for Series / Sequences: Identifying and defining elements

Exercise #1

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

Video Solution

Step-by-Step Solution

It is possible to see that there is a difference of one number between each number.

That is, 1 is added to each number and it will be the next number:

1+1=2 1+1=2

2+1=3 2+1=3

3+1=4 3+1=4

Etcetera. Therefore, the next numbers missing in the sequence will be:8+1=9 8+1=9

10+1=11 10+1=11

Answer

11 , 9

Exercise #2

Look at the following set of numbers and determine if there is any property, if so, what is it?

94,96,98,100,102,104 94,96,98,100,102,104

Video Solution

Step-by-Step Solution

One can observe that the difference between each number is 2.

That is, with each leap the next number increases by 2:

94+2=96 94+2=96

96+2=98 96+2=98

98+2=100 98+2=100

and so forth......

Answer

+2 +2

Exercise #3

The table shows the number of balls and the number of courts at the school:

246123BallsCourts

.

Complete:

Number of balls is _________ than the number of courts

Video Solution

Step-by-Step Solution

It is possible to see that if you multiply each number from the right column by 2, you get the number from the left column.

That is:1×2=2 1\times2=2

2×2=4 2\times2=4

3×2=6 3\times2=6

Therefore, the number of balls is 2 times greater than the number of courts.

Answer

2 times greater

Exercise #4

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

Video Solution

Answer

Yes

Exercise #5

Look at the following set of numbers and determine if there is any property, if so, what is it?

10,8,6,4,2 10,8,6,4,2

Video Solution

Answer

2 -2

Exercise #6

Look at the following set of numbers and determine if there is any property, if so, what is it?

1,2,3,4,5,6 1,2,3,4,5,6

Video Solution

Answer

+1 +1

Exercise #7

Look at the following set of numbers and determine if there is any property, if so, what is it?

13,10,7,4,1 13,10,7,4,1

Video Solution

Answer

3 -3

Exercise #8

Look at the following set of numbers and determine if there is any property, if so, what is it?

13,16,20,23 13,16,20,23

Video Solution

Answer

Does not exist

Exercise #9

Look at the following set of numbers and determine if there is a rule. If there is one, what is it?

5,10,15,20,25,30 5,10,15,20,25,30

Video Solution

Answer

+5 +5

Exercise #10

Look at the following set of numbers and determine if there is any property, if so, what is it?

100,50,25,10,20 100,50,25,10,20

Video Solution

Answer

Does not exist

Exercise #11

Look at the following set of numbers and determine if there is any property, if so, what is it?

12,24,35,48,60 12,24,35,48,60

Video Solution

Answer

Does not exist

Exercise #12

Look at the following set of numbers and determine if there is any property, if so, what is it?

1,3,9,26,81 1,3,9,26,81

Video Solution

Answer

Does not exist

Exercise #13

Look at the following set of numbers and determine if there is any property, if so, what is it?

2,4,8,16,32,64 2,4,8,16,32,64

Video Solution

Answer

×2 \times2

Exercise #14

Look at the following set of numbers and determine if there is any property, if so, what is it?

256,64,16,4,1 256,64,16,4,1

Video Solution

Answer

×0.25 \times0.25

Exercise #15

Look at the following set of numbers and determine if there is any property, if so, what is it?

4,8,12,5,20 4,8,12,5,20

Video Solution

Answer

Does not exist

Exercise #16

Look at the following set of numbers and determine if there is any property, if so, what is it?

88,66,44,22,2 88,66,44,22,2

Video Solution

Answer

Does not exist

Exercise #17

Is there a common difference?

Is the sequence descending or ascending?

2- , 1- , 0 , 1 , 2 , 3 , 4

Video Solution

Answer

Yes, descending.

Exercise #18

Is there a rule to the following sequence? If so, then what is it?

768 , 192 , 48 , 12 , 3

Video Solution

Answer

Yes, multiply by 4.

Exercise #19

Look at the following sequence:

64 , 85 , 98 , 100 , 1

Is there a term-to-term rule?

Video Solution

Answer

No.

Exercise #20

Look at the following set of numbers and determine if there is any property, if so, what is it?

2,5,12.5,31.25 2,5,12.5,31.25

Video Solution

Answer

×2.5 \times2.5