Arithmetic and Geometric Sequences

How can you determine if a sequence is geometric?

• A sequence is geometric if the ratio of consecutive terms is constant.

• A sequence is geometric if the difference between consecutive terms is constant.

• A sequence is geometric if the sum of the terms is constant.

• A sequence is geometric if the product of the terms is constant.

What is the significance of the first term in a sequence?

• It is the last term in the sequence.

• It serves as the starting point for calculating subsequent terms in both arithmetic and geometric sequences.

• It is irrelevant to the sequence.

• It determines the common difference in arithmetic sequences.

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

• @@a_n = a_1 \times r^{(n-1)}@@

• @@a_n = a_1 + (n-1) \times r@@

• @@a_n = a_1 \div r^{(n-1)}@@

• @@a_n = a_1 \times n \times r@@

Identify the common ratio in the sequence 1, 3, 9, 27, ...

• 1

• 2

• 3

• 4

What is an arithmetic sequence?

• A sequence of numbers where each term is the sum of the previous two terms.

• A sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

• A sequence of numbers that follows a geometric progression.

• A sequence of numbers that increases exponentially.

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

• By adding any term to the subsequent term: @@d = a_{n+1} + a_n@@

• By multiplying any term by the subsequent term: @@d = a_{n+1} imes a_n@@

• By subtracting any term from the subsequent term: @@d = a_{n+1} - a_n@@

• By dividing any term by the subsequent term: @@d = rac{a_{n+1}}{a_n}@@

What is the 4th term of the geometric sequence 2, 6, 18, ...?

• 36

• 54

• 72

• 18

What is the explicit formula for the geometric sequence 3, 6, 12, 24, ...?

• @@a_n = 3 imes 2^{(n-1)}@@

• @@a_n = 3 imes 3^{(n-1)}@@

• @@a_n = 6 imes 2^{(n-1)}@@

• @@a_n = 3 imes 4^{(n-1)}@@

What is the formula for the nth term of an arithmetic sequence?

• @@a_n = a_1 + (n-1)d@@

• @@a_n = a_1 + nd@@

• @@a_n = a_1 + (n+1)d@@

• @@a_n = a_1 - (n-1)d@@

What is the explicit formula for the arithmetic sequence 2, 5, 8, 11, ...?

• @@a_n = 2 + (n-1) \times 3@@

• @@a_n = 2 + (n-1) \times 2@@

• @@a_n = 2 + (n-1) \times 4@@

• @@a_n = 2 + (n-1) \times 5@@