Arithmetic and Geometric Sequences Quiz

What is the main difference between arithmetic and geometric sequences?

• Arithmetic sequences have a multiplicative pattern, while geometric sequences have an additive pattern.

• Arithmetic sequences have an additive pattern, while geometric sequences have a multiplicative pattern.

• Both sequences have the same pattern.

• Arithmetic sequences are always increasing, while geometric sequences are always decreasing.

In an arithmetic sequence, what is the term used to describe the constant difference between consecutive terms?

• Common ratio

• Common difference

• Common factor

• Common sum

Which formula represents the explicit formula for an arithmetic sequence?

• a_n = a_1 / r^(n-1)

• a_n = a_1 - (n-1) * d

• a_n = a_1 + (n-1) * d

• a_n = a_1 * r^(n-1)

In a geometric sequence, what is the term used to describe the constant factor between consecutive terms?

• Common ratio

• Common difference

• Common product

• Common sum

Which formula represents the explicit formula for a geometric sequence?

• a_n = a_1 / r^(n-1)

• a_n = a_1 * r^(n-1)

• a_n = a_1 - (n-1) * d

• a_n = a_1 + (n-1) * d

How can you determine if a sequence is neither arithmetic nor geometric?

• If the sequence is decreasing.

• If the sequence is increasing.

• If there is no common difference or common ratio.

• If the sequence has a common sum.

What is the first term of the sequence if the common difference is 15 and the second term is 30?

• 60

• 30

• 15

• 45

If a sequence has a first term of 12 and a common ratio of -6, what is the second term?

• 12

• -12

• 72

• -72

What is the explicit formula for an arithmetic sequence with a first term of 17 and a common difference of -10?

• a_n = 17 + (n-1) * -10

• a_n = 17 - (n-1) * -10

• a_n = 17 - (n-1) * 10

• a_n = 17 + (n-1) * 10

If a sequence oscillates between positive and negative values, what type of sequence is it likely to be?

• Neither

• Geometric

• Both

• Arithmetic