Sequences and Series Problems

The video tutorial explores various types of number sequences, starting with arithmetic sequences where terms increase or decrease by a constant amount. It then moves to geometric sequences, characterized by multiplication or division. The tutorial also covers sequences involving exponents, such as squares and cubes, and more complex patterns that require identifying relationships between terms. Additionally, fractional sequences are discussed, demonstrating how to separate numerators and denominators to find patterns. The video concludes with tips for identifying sequence patterns.

What is the next term in the arithmetic sequence: 5, 9, 13, 17?

• 19

• 29

• 25

• 21

In an arithmetic sequence, if the first term is 3 and the common difference is 4, what is the fifth term?

• 27

• 23

• 19

• 15

What is the next term in the geometric sequence: 2, 6, 18, 54?

• 162

• 324

• 216

• 108

If a geometric sequence starts with 4 and has a common ratio of 3, what is the fourth term?

• 12

• 36

• 324

• 108

What is the next term in the sequence of squares: 1, 4, 9, 16?

• 30

• 24

• 20

• 25

In a sequence of cubes, if the first term is 1 and the second term is 8, what is the fourth term?

• 216

• 64

• 27

• 125

What is the next term in the sequence: 1, 1, 2, 3, 5, 8?

• 10

• 13

• 11

• 12

In the sequence: 2, 3, 5, 8, 12, what is the pattern used to find the next term?

• Add 1, 2, 3, 4

• Multiply by 2

• Add 2, 3, 4, 5

• Subtract 1, 2, 3, 4

What is the next term in the fractional sequence: 1/2, 2/3, 3/4?

• 5/6

• 4/5

• 6/7

• 7/8

In the sequence: 3/5, 4/7, 5/9, what is the pattern for the numerators?

• Multiply by 3

• Multiply by 2

• Add 2

• Add 1