Question

A)

Multiple Choice
What are the next two terms of the following sequence? 1, 5, 9, …
(1 point)
27, 211
10, 11
12, 15
13, 17

Answer 1

[AI-generated answer — Bot GPT 3.5]

The next number in the sequence can be found by adding 4 to each number:

1 + 4 = 5
5 + 4 = 9
9 + 4 = 13

Therefore, the next two terms of the sequence are 13 and 17.

Answer 2

A)

What is the common difference of the following arithmetic sequence?
102, 100, 98, 96…
(1 point)
2
–2
–1
102

Answer 3

[AI-generated answer — Bot GPT 3.5]

The common difference of an arithmetic sequence is the constant value that is added or subtracted to each term to obtain the next term.

In the given sequence, each term is decreasing by 2. Therefore, the common difference is -2.

So, the correct answer is -2.

Answer 4

A)

What is the ninth term of the arithmetic sequence defined by the rule below?
A(n) = –14 + (n – 1)(2)
(1 point)
232
230
2
4

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the ninth term of an arithmetic sequence, we need to substitute n = 9 into the given rule:

A(n) = -14 + (n - 1)(2)
A(9) = -14 + (9 - 1)(2)
A(9) = -14 + 8(2)
A(9) = -14 + 16
A(9) = 2

Therefore, the ninth term of the arithmetic sequence defined by the rule is 2.

Answer 6

A)

Which function below represents the arithmetic sequence 3, 7, 11, 15...?
(1 point)
f(n) = 4 + 3(n – 1)
f(n) = 4 + 3n
f(n) = 3 + 4n
f(n) = 3 + 4(n – 1)

Answer 7

[AI-generated answer — Bot GPT 3.5]

The common difference of the arithmetic sequence is 4 because each term is obtained by adding 4 to the previous term.

To find the function that represents the arithmetic sequence, we start with the general form of an arithmetic sequence:

f(n) = a + d(n - 1)

where a represents the first term and d represents the common difference.

In this case, the first term is 3 and the common difference is 4.

Plugging these values into the general form, we get:

f(n) = 3 + 4(n - 1)

Therefore, the function that represents the arithmetic sequence 3, 7, 11, 15... is:

f(n) = 3 + 4(n - 1)