Arithmetic and Geometric Sequences

What is an arithmetic sequence?

• A sequence of numbers where each term is multiplied by a constant factor.

• A sequence of numbers in which the difference between consecutive terms is constant.

• A sequence of numbers that follows a geometric pattern.

• A sequence of numbers that increases exponentially.

Find the 5th term of the geometric sequence: 2, 6, 18, ...

• 162

• 486

• 324

• 648

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 15th term?

• 31

• 33

• 35

• 37

Find the 10th term of the arithmetic sequence: 3, 7, 11, ...

• 35

• 39

• 45

• 33

What is the common difference of the sequence: 10, 15, 20, 25?

• 3

• 4

• 5

• 6

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

• a_n = a_1 + (n-1)d

• a_n = a_1 * n + d

• a_n = a_1 - (n-1)d

• a_n = d/n + a_1

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

• By adding any term to the previous term: r = a_n + a_(n-1).

• By multiplying any term by the previous term: r = a_n * a_(n-1).

• By dividing any term by the previous term: r = a_n / a_(n-1).

• By subtracting any term from the previous term: r = a_n - a_(n-1).

What are the next two terms of the sequence: 5, 15, 45, 135?

• 405 and 1215

• 300 and 900

• 250 and 750

• 500 and 1500

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 6th term?

• 64

• 48

• 96

• 72

What is the common ratio of the sequence: 4, 12, 36, 108?

• 1

• 2

• 3

• 4