Gr12 Mathematics: Ch 1.2 Geometric Sequences

Play an AI-generated podcast conversation about this lesson

What is the definition of a geometric sequence?

A sequence of numbers where each term after the first is found by multiplying the previous term by a constant value. (correct)

A sequence of numbers where each term after the first is found by adding a constant value.

A sequence of numbers where each term after the first is found by dividing the previous term by a constant value.

A sequence of numbers where each term after the first is found by subtracting a constant value.

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

Tn = ar^(n+1)

Tn = ar^(2n-1)

Tn = ar^(n-1) (correct)

Tn = ar^n

How do you find the common ratio (r) of a geometric sequence?

r = Tn / (n-1)

r = Tn / T(n-1) (correct)

r = Tn - T(n-1)

r = Tn + T(n-1)

What is the geometric mean between two numbers a and b?

sqrt(ab) Signup and view all the answers

What is the characteristics of a geometric sequence when r > 1?

The sequence grows exponentially. Signup and view all the answers

How do you test if a sequence is geometric?

Calculate the ratios between consecutive terms. Signup and view all the answers

What is the graphical representation of a geometric sequence?

An exponential graph. Signup and view all the answers

What happens to the terms of a geometric sequence when r is negative?

The terms alternate in sign. Signup and view all the answers

What is the value of the second term in a geometric sequence if the first term is 3 and the common ratio is 2?

6 Signup and view all the answers

A geometric sequence has a first term of 4 and a common ratio of 3. What is the value of the fourth term?

81 Signup and view all the answers

Which of the following sequences is geometric?

2, 4, 8, 16 Signup and view all the answers

What is the value of n in a geometric sequence if the first term is 2, the common ratio is 3, and the nth term is 486?

7 Signup and view all the answers

A geometric sequence has a first term of -2 and a common ratio of -3. What is the sign of the fifth term?

Positive Signup and view all the answers

Which of the following statements is true about a geometric sequence with a common ratio between 0 and 1?

The sequence decays exponentially Signup and view all the answers

What is the value of the common ratio in a geometric sequence if the first term is 5 and the second term is 15?

3 Signup and view all the answers

A geometric sequence has a first term of 1 and a common ratio of 2. How many terms are in the sequence if the 10th term is 1024?

10 Signup and view all the answers

If a geometric sequence has a first term of 2 and a common ratio of 4, what is the value of the seventh term?

16384 Signup and view all the answers

If a geometric sequence has a first term of 3 and a common ratio of -2, what is the value of the fifth term?

-96 Signup and view all the answers

A geometric sequence has a first term of 5 and a common ratio of 1/2. How many terms are in the sequence if the 8th term is 5/128?

8 Signup and view all the answers

If a geometric sequence has a first term of -1 and a common ratio of 3, what is the value of the geometric mean between the first term and the fourth term?

sqrt(81) Signup and view all the answers

A geometric sequence has a first term of 2 and a common ratio of 1/3. What is the value of the sixth term?

2/729 Signup and view all the answers

If a geometric sequence has a first term of 4 and a common ratio of -1, what is the value of the 10th term?

4 Signup and view all the answers

A geometric sequence has a first term of 1 and a common ratio of 2. What is the value of the geometric mean between the first term and the fifth term?

sqrt(32) Signup and view all the answers

If a geometric sequence has a first term of -2 and a common ratio of 5, what is the value of the eighth term?

-390625 Signup and view all the answers