Understanding Geometric Sequences

What is a geometric sequence?

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

• A geometric sequence is a sequence of numbers that increases by a fixed amount each time.

• A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a constant ratio.

• A geometric sequence is a random arrangement of numbers without any specific pattern.

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

• Multiply any term by the previous term.

• Add the first term to the last term.

• Subtract the previous term from the next term.

• Divide any term by the previous term.

If the first term is 3 and the common ratio is 2, what is the 5th term?

• 48

• 60

• 36

• 24

If a geometric series has a first term of 5 and a common ratio of 1/2, what is the sum of the first 4 terms?

• 10.5

• 7.25

• 12.0

• 9.375

What happens to the sum of a geometric series as the number of terms approaches infinity when the common ratio is less than 1?

• The sum approaches 0 as the number of terms approaches infinity.

• The sum becomes negative as the number of terms increases.

• The sum approaches a / (1 - r) as the number of terms approaches infinity.

• The sum diverges to infinity as the number of terms increases.

Can a geometric sequence have a negative common ratio? Give an example.

• Example: 1, 2, 4, 8 with a common ratio of 2.

• No, a geometric sequence cannot have a negative common ratio.

• Yes, a geometric sequence can have a negative common ratio. Example: 2, -6, 18, -54 with a common ratio of -3.

• A geometric sequence must always have a positive common ratio.

What is the difference between a geometric sequence and a geometric series?

• A geometric sequence is the sum of numbers; a geometric series is a list of those numbers.

• A geometric sequence is a list of numbers; a geometric series is the sum of those numbers.

• A geometric sequence is always finite; a geometric series is always infinite.

• A geometric sequence has a constant difference; a geometric series has a variable difference.

If the first term of a geometric sequence is 10 and the common ratio is 3, what is the 6th term?

• 7290

• 2430

• 810

• 1200

How do you identify whether a sequence is geometric?

• A sequence is geometric if all terms are positive numbers.

• 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 consecutive terms is constant.

What is the sum of an infinite geometric series with a first term of 4 and a common ratio of 1/3?

• 10

• 6

• 8

• 12