Arithmetic and Geometric Sequences

The video tutorial covers arithmetic and geometric sequences. It begins by explaining arithmetic sequences, where the difference between consecutive terms is constant, and provides a general formula. Two examples are given: one to find the general formula and another to calculate a specific term. The tutorial then introduces geometric sequences, where the ratio between consecutive terms is constant, and demonstrates how to calculate a specific term using an example.

What is the defining characteristic of an arithmetic sequence?

• The product of consecutive terms is constant.

• The ratio between consecutive terms is constant.

• The difference between consecutive terms is constant.

• The sum of consecutive terms is constant.

In the sequence 8, 11, 14, 17, what is the common difference?

• 2

• 5

• 3

• 4

If the first term of an arithmetic sequence is 8 and the common difference is 3, what is the 5th term?

• 17

• 26

• 20

• 23

What is the value of 'b' in the formula for the arithmetic sequence with the first term 8 and common difference 3?

• 8

• 5

• 3

• 2

What is the 23rd term of the arithmetic sequence with the first term 7 and common difference 4?

• 95

• 91

• 87

• 99

What is the defining characteristic of a geometric sequence?

• The difference between consecutive terms is constant.

• The ratio between consecutive terms is constant.

• The sum of consecutive terms is constant.

• The product of consecutive terms is constant.

In the geometric sequence 6, 12, 24, 48, what is the common ratio?

• 6

• 4

• 3

• 2

If the first term of a geometric sequence is 6 and the common ratio is 2, what is the 4th term?

• 48

• 192

• 24

• 96

What is the 10th term of the geometric sequence with the first term 6 and common ratio 2?

• 512

• 3072

• 1024

• 2048

In a geometric sequence, if the first term is 6 and the common ratio is 2, what is the 9th term?

• 1024

• 512

• 2048

• 256