Exploring Arithmetic and Geometric Sequences

What is the common difference in an arithmetic sequence?

• The variable used to represent terms

• The initial term of the sequence

• The constant value added to each term

• The rate at which terms decrease

What does the variable 'd' represent in arithmetic sequences?

• The common ratio

• The nth term of the sequence

• The first term of the sequence

• The common difference

How is the nth term of an arithmetic sequence calculated?

• Using the formula a_n = a_1 + (n - 1) * d

• By adding the common difference to the first term n times

• By dividing the last term by the common difference

• By multiplying the common difference by n

In an arithmetic sequence, if the first term is 3 and the common difference is 2, what is the fourth term?

• 5

• 7

• 11

• 9

What characterizes a geometric sequence?

• A constant sum between consecutive terms

• A pattern created by adding a common difference

• A pattern created by multiplying by a common ratio

• A sequence that can be graphed as a straight line

How do you find the common ratio in a geometric sequence?

• By adding consecutive terms

• By dividing a term by its preceding term

• By calculating the slope of the sequence

• By subtracting the first term from the second term

If a geometric sequence has a first term of 1 and a common ratio of -4, what is the third term?

• 64

• -64

• -16

• 16

For the geometric sequence -3, 15, -75, what is the common ratio?

• 3

• -3

• -5

• 5

What is the formula for the nth term of a geometric sequence?

• a_n = a_1 - r^(n - 1)

• a_n = a_1 * r^(n - 1)

• a_n = a_1 + (n - 1) * r

• a_n = a_1 / r^(n - 1)

Using the formula for the nth term of a geometric sequence, what is the 9th term of the sequence -6, 12, -24, if the common ratio is -2?

• -768

• 768

• -1536

• 1536