Understanding Sequences

The video tutorial explains how to find the next term in a sequence by identifying patterns. It covers arithmetic sequences, which have a common difference, and geometric sequences, which have a common ratio. The video provides multiple examples of each type of sequence, demonstrating how to calculate subsequent terms. It also discusses identifying patterns in sequences that do not fit neatly into arithmetic or geometric categories, including sequences involving fractions. The tutorial concludes with a summary and additional resources for further learning.

What is the next number in the arithmetic sequence: 2, 5, 8, 11, 14?

• 16

• 17

• 18

• 19

In an arithmetic sequence, if the common difference is 4, what is the next number after 17?

• 22

• 21

• 20

• 23

What is the next number in the geometric sequence: 3, 6, 12, 24?

• 54

• 42

• 36

• 48

If a geometric sequence has a common ratio of 3, what is the next number after 36?

• 72

• 108

• 144

• 96

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

• 30

• 25

• 24

• 20

In the sequence of cubes: 8, 27, 64, what is the next number?

• 81

• 150

• 100

• 125

What is the next number in the sequence with increasing differences: 4, 6, 9, 13, 18?

• 25

• 24

• 23

• 22

In a sequence where differences increase by 2, what is the next number after 27?

• 37

• 35

• 41

• 39

What is the next fraction in the sequence: 3/4, 5/7, 7/10, 9/13?

• 11/16

• 11/15

• 11/14

• 11/13

In the sequence of fractions: 11/4, 8/9, 5/16, what is the next fraction?

• 2/25

• 3/25

• 4/25

• 5/25