Exploring Arithmetic and Geometric Sequences

What is the common difference in the given arithmetic sequence example?

• 2

• 5

• 10

• 7

What defines an arithmetic sequence?

• Each term differs from the next by a constant amount.

• Each term is multiplied by a constant to get the next term.

• Each term is the square of the previous term.

• Each term is divided by a constant to get the next term.

How do you find the common difference in an arithmetic sequence?

• Subtract the first term from the second term.

• Divide any term by the previous term.

• Subtract the second term from the third term.

• Subtract any term from the next term.

What is the common ratio in a geometric sequence?

• The sum of any two consecutive terms.

• The difference between any two consecutive terms.

• The result of dividing any term by its preceding term.

• The result of multiplying any term by its preceding term.

In the context of geometric sequences, what does 'r' stand for?

• The nth term

• The common difference

• The common ratio

• The first term

What characteristic is unique to geometric sequences?

• A constant subtraction between consecutive terms.

• A constant ratio between consecutive terms.

• A constant difference between consecutive terms.

• A constant sum between consecutive terms.

How can the nth term of an arithmetic sequence be calculated?

• By dividing the first term by the common difference raised to the power of (n-1).

• By subtracting the common difference from the first term (n-1) times.

• By adding the first term to the product of (n-1) and the common difference.

• By multiplying the first term by the common difference raised to the power of (n-1).

What formula is used to calculate the sum of the first n terms in an arithmetic sequence?

• n multiplied by the sum of the first term and the nth term, all divided by 2.

• The product of the common difference and the nth term.

• The sum of the common difference and the nth term.

• The first term raised to the power of n.

Why are arithmetic sequences considered important?

• They are the basis for all mathematical operations.

• They provide a systematic way to understand patterns and solve problems.

• They offer a method to predict stock market trends.

• They can only be used to find the sum of terms.