Exploring Arithmetic and Geometric Sequences

What is a sequence?

• A single number repeated multiple times

• A list of numbers with a specific pattern

• A graphical representation of data

• A mathematical operation like addition or subtraction

How can you predict the next term in an arithmetic sequence?

• By dividing the previous term

• By subtracting a constant from the previous term

• By multiplying the previous term by a constant

• By adding a constant to the previous term

How do you find the nth term in an arithmetic sequence?

• By dividing the last term by n

• By using the formula an = a1 + (n - 1)d

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

• By multiplying the first term by n

What is the common difference in an arithmetic sequence?

• The difference between any term and the next

• The sum of the first and last term

• The product of the first two terms

• The ratio of any two consecutive terms

What is a recursive equation?

• A formula that calculates the sum of a sequence

• An equation that only applies to geometric sequences

• An equation that defines each term based on the previous term

• An equation that can predict any term without knowing the previous ones

What is the purpose of using an explicit equation in sequences?

• To identify the pattern of the sequence

• To find any term in the sequence without calculating all previous terms

• To graph the sequence on a coordinate plane

• To define the sequence in terms of itself

Can arithmetic sequences decrease?

• Yes, but only if they are infinite

• No, they can only increase

• Yes, if the common difference is negative

• No, because they are defined by addition

What distinguishes a geometric sequence from an arithmetic sequence?

• The use of addition in arithmetic and subtraction in geometric

• The ability to use recursive equations in geometric sequences only

• The linear growth in arithmetic and exponential in geometric

• The constant ratio in geometric versus the constant difference in arithmetic

In a geometric sequence, what does the term 'common ratio' refer to?

• The sum of all terms in the sequence

• The ratio between any two consecutive terms

• The difference between any two consecutive terms

• The total number of terms in the sequence

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

• an = a1^n * r

• an = a1 + d(n-1)

• an = a1 * r^(n-1)

• an = a1 / r^(n-1)