Arithmetic & Geometric Sequences

The video tutorial explains the differences between arithmetic and geometric sequences. Arithmetic sequences involve adding or subtracting a constant number, while geometric sequences involve multiplying or dividing by a constant factor. Examples are provided for both types of sequences, illustrating how arithmetic sequences change linearly and geometric sequences change exponentially. The video concludes with a comparison of the two, highlighting how geometric sequences grow or shrink more rapidly than arithmetic sequences.

What is the defining characteristic of an arithmetic sequence?

• Multiplying by a constant factor

• Adding or subtracting a constant number

• Dividing by a constant factor

• Adding a variable number

In an arithmetic sequence starting with 5 and subtracting 7 each time, what is the third term?

• -2

• -16

• -23

• -9

What operation is primarily used in a geometric sequence?

• Exponentiation

• Multiplication

• Subtraction

• Addition

If a geometric sequence starts at 100 and is divided by 2 each time, what is the second term?

• 6.25

• 50

• 25

• 12.5

How do geometric sequences differ from arithmetic sequences in terms of growth?

• Geometric sequences grow or shrink at a constant rate

• Arithmetic sequences grow or shrink exponentially

• Geometric sequences grow or shrink more rapidly

• Arithmetic sequences grow or shrink more rapidly