Question

The following arithmetic sequence is given.

14, 11, 8, 5, ...

What are the next three terms?
A.4, 3, 2

B.2, −1, −4

C.3, 1, −2

D.1, −1, −3

Answer 1

an = 3n + 17

B.an = −3n + 17

C.an = 3n − 17

D.an = 17n − 3

Answer 2

To find the next three terms in the arithmetic sequence 14, 11, 8, 5, we first need to identify the common difference.

The common difference is calculated as follows:

11 - 14 = -3
8 - 11 = -3
5 - 8 = -3

So, the common difference is -3.

Now, to find the next three terms, we will continue subtracting 3 from the last term:

1. 5 - 3 = 2
2. 2 - 3 = -1
3. -1 - 3 = -4

Thus, the next three terms of the sequence are 2, -1, and -4.

Therefore, the answer is **B. 2, −1, −4.**

Answer 3

It seems like you've provided several expressions for a general term of a sequence, denoted as \( a_n \). However, you've not given the context for what you're asking.

Let’s analyze each option:

1. **A. \( a_n = 3n + 17 \)**
This represents a linear expression where the term increases by 3 for each subsequent value of \( n \).

2. **B. \( a_n = -3n + 17 \)**
This also represents a linear expression but decreases by 3 for each subsequent value of \( n\).

3. **C. \( a_n = 3n - 17 \)**
This is another linear expression that increases by 3 for each value of \( n \) but starts from -17 instead of 17.

4. **D. \( a_n = 17n - 3 \)**
This expression increases by 17 for each value of \( n\), starting from -3.

If you could clarify the question or provide a specific context for these expressions (like a problem statement or further instructions), I’d be happy to help you!