Different Sequences Quiz Lessons 1-3

15, __, __, 405... What are the missing terms?

(Separate your answers with a comma and a space)

Ex: 6, 7

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

Which variable represents the common ratio?

• r

• n

• a₁

• a_n

Answer explanation

The common ratio in a geometric sequence is represented by the variable 'r'. It defines the factor by which each term is multiplied to get the next term, distinguishing it from other variables like 'n', 'a1', and 'an'.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

What is the first term of the sequence below?

6, 9, 12, 15, ...

• 3

• 6

• 9

• 12

Answer explanation

The first term of the sequence is 6. The sequence starts with 6, followed by 9, 12, and 15, indicating that 6 is indeed the first term.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

What is the common difference of the sequence below?

6, 9, 12, 15, ...

Hint: Common difference means the ADDING pattern

• 3

• 6

• 9

• 12

Answer explanation

To find the common difference, subtract the first term from the second: 9 - 6 = 3. This pattern continues (12 - 9 = 3, 15 - 12 = 3), confirming the common difference is 3.

Tags

CCSS.HSF.BF.A.2

What is the tenth term in the arithmetic sequence:

12, 19, 26, 33, ...

Hint: Find the common difference and then either continue the pattern or write and use an explicit formula.

• 47

• 61

• 75

• 96

Answer explanation

The common difference is 7 (19-12). The nth term formula is a_n = 12 + (n-1) * 7. For n=10, a_10 = 12 + 9 * 7 = 12 + 63 = 75. Thus, the tenth term is 75.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

Which of the following is a geometric sequence?

• 3, 6, 9, 12, 15, …

• 2, 6, 18, 54, 162, …

• . 5, 8, 11, 14, 17, …

• 4, 8, 12 ,16, 20, …

Answer explanation

A geometric sequence has a constant ratio between consecutive terms. In the sequence 2, 6, 18, 54, 162, each term is multiplied by 3 to get the next term, making it a geometric sequence.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Which of the following is NOT a geometric sequence?

• 5, 10, 20, 40, 80, …

• 2, 6, 18, 54, 162, …

• 5, 8, 11, 14, 17, …

• 3, 6, 12, 24, 48, …

Answer explanation

The sequence 5, 8, 11, 14, 17, … is an arithmetic sequence, not a geometric one, as it adds a constant (3) rather than multiplying by a common ratio.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

What is the common ratio of the geometric sequence 5, 10, 20, 40?

• 2

• 5

• 10

• 20

Answer explanation

In a geometric sequence, each term is multiplied by the common ratio to get the next term. Here, 10/5 = 2, 20/10 = 2, and 40/20 = 2. Thus, the common ratio is 2.

Tags

CCSS.HSF.BF.A.2

Find the 8^th term of the geometric sequence 3, 6, 12, …

• 42

• 128

• 384

• 768

Answer explanation

The sequence is geometric with a common ratio of 2. The 8th term can be found using the formula a_n = a_1 * r^(n-1). Here, a_1 = 3, r = 2, and n = 8. Thus, a_8 = 3 * 2^(8-1) = 3 * 128 = 384.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

Observe the sequence

1, 2, 4, 8, 16,...

What is rule or pattern?

• add 2

• minus 2

• multiply 2

• divide 2

Answer explanation

The sequence doubles each term: 1x2=2, 2x2=4, 4x2=8, 8x2=16. Thus, the pattern is to multiply by 2, making 'multiply 2' the correct choice.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2