Differences Between Arithmetic and Geometric Sequences

What is the correct way to denote the first term in a sequence?

• a1

• A1

• a_1

• A_1

What does the subscript in a sequence notation typically represent?

• The sequence number

• The common difference

• The common ratio

• The term number

What is the common difference in the sequence 3, 7, 11, 15, 19?

• 2

• 4

• 6

• 8

Which sequence type has a constant rate of change?

• Arithmetic sequence

• Geometric sequence

• Both arithmetic and geometric

• Neither

Which formula is used to find the nth term in an arithmetic sequence?

• a_n = a_1 + n / d

• a_n = a_1 + (n - 1) * d

• a_n = a_1 / (n - 1) * d

• a_n = a_1 * r^(n - 1)

What operation characterizes a geometric sequence?

• Division

• Multiplication

• Subtraction

• Addition

What is the common ratio in the sequence 3, 6, 12, 24?

• 6

• 4

• 3

• 2

In a geometric sequence, if the first term is 5 and the common ratio is 3, what is the third term?

• 35

• 15

• 45

• 40

How do you calculate the fifth term in a geometric sequence using the explicit formula?

• a_5 = a_1 + 4 * r

• a_5 = a_1 * r^4

• a_5 = a_1 + (5 - 1) * r

• a_5 = a_1 * r^(5 - 1)

What is the primary difference between arithmetic and geometric sequences?

• Arithmetic sequences use addition or subtraction, geometric use multiplication or division.

• There is no difference; both sequence types use the same operations.

• Arithmetic sequences use multiplication, geometric use addition.

• Arithmetic sequences use addition, geometric use division.