Identifying Arithmetic and Geometric Sequences

What is the sequence called when each term is obtained by adding a constant value to the previous term?

• Recursive sequence

• Exponential sequence

• Geometric sequence

• Arithmetic sequence

What is the common difference in an arithmetic sequence?

• The value you multiply by to get the next term

• The value you add to get the next term

• The first term of the sequence

• The ratio between consecutive terms

How do you find the 10th term of an arithmetic sequence given the first term and common difference?

• Multiply the common difference by 10

• Add the common difference to the first term 9 times

• Use the explicit formula with n=10

• Divide the first term by the common difference

What defines a geometric sequence?

• Subtracting a constant value from each term

• Adding a constant value to each term

• Multiplying each term by a constant value

• Dividing each term by a constant value

What is the common ratio in a geometric sequence?

• The difference between consecutive terms

• The sum of the first two terms

• The value each term is multiplied by to get the next term

• The quotient of any term and its predecessor

How do you find the 100th term of a geometric sequence?

• Multiply the first term by the common ratio 100 times

• Use the explicit formula with n=100

• Add the common ratio to the first term 99 times

• Raise the common ratio to the power of 100

What is a recursive formula?

• A formula that allows you to find any term in the sequence without knowing the previous terms

• A formula that requires the knowledge of the previous term(s) to find the next term

• A formula that only applies to geometric sequences

• A formula that calculates the sum of a sequence

How is a recursive formula for an arithmetic sequence structured?

• F(n) = a * r^(n-1)

• F(n) = a + (n-1)d

• F(n) = F(n-1) + d

• F(n) = F(n-1) * d

In a geometric sequence, if the common ratio is 3, what is the recursive formula to find the 5th term?

• F(5) = 5 * 3

• F(5) = 3F(4)

• F(5) = F(4) + 3

• F(5) = 3^5

What is necessary to use a recursive formula effectively?

• Knowing the first term of the sequence

• Having the explicit formula

• Knowing at least one term in the sequence

• Knowing the common difference or ratio