Question

Which of the following correctly uses the explicit formula, An=14+(n−1)⋅1/2 , to find the 9th term of the described arithmetic sequence?

Answer 1

Which of the following correctly uses the explicit formula, An=14+(n−1)⋅1/2 , to find the 9th term of the described arithmetic sequence?(1 point)
Responses

814
8 Start Fraction 1 over 4 End Fraction

834
8 Start Fraction 3 over 4 End Fraction

414
4 Start Fraction 1 over 4 End Fraction

434

Answer 2

Which of the following correctly uses the explicit formula, An=1/4+(n−1)⋅1/2 , to find the 9th term of the described arithmetic sequence?(1 point)
Responses

814
8 Start Fraction 1 over 4 End Fraction

834
8 Start Fraction 3 over 4 End Fraction

414
4 Start Fraction 1 over 4 End Fraction

434

Answer 3

To find the 9th term of the arithmetic sequence using the given explicit formula:

\[
A_n = 14 + (n - 1) \cdot \frac{1}{2}
\]

we need to substitute \( n = 9 \) into the formula.

1. Substitute \( n = 9 \):

\[
A_9 = 14 + (9 - 1) \cdot \frac{1}{2}
\]

2. Calculate \( 9 - 1 \):

\[
9 - 1 = 8
\]

3. Now substitute this value back into the equation:

\[
A_9 = 14 + 8 \cdot \frac{1}{2}
\]

4. Calculate \( 8 \cdot \frac{1}{2} \):

\[
8 \cdot \frac{1}{2} = 4
\]

5. Finally, add this to 14:

\[
A_9 = 14 + 4 = 18
\]

Thus, the 9th term of the arithmetic sequence is \( A_9 = 18 \).

Answer 4

Let's evaluate the explicit formula \( A_n = 14 + (n - 1) \cdot \frac{1}{2} \) to find the 9th term, as we computed earlier:

1. **Substitute \( n = 9 \)**:
\[
A_9 = 14 + (9 - 1) \cdot \frac{1}{2}
\]

2. **Calculate \( 9 - 1 \)**:
\[
9 - 1 = 8
\]

3. **Substitute this value**:
\[
A_9 = 14 + 8 \cdot \frac{1}{2}
\]

4. **Calculate \( 8 \cdot \frac{1}{2} \)**:
\[
8 \cdot \frac{1}{2} = 4
\]

5. **Finally, add this to 14**:
\[
A_9 = 14 + 4 = 18
\]

Now, looking at your response options:

1. \( 814 \) (equivalent to \( 8 \frac{1}{4} \), or 8.25)
2. \( 834 \) (equivalent to \( 8 \frac{3}{4} \), or 8.75)
3. \( 414 \) (equivalent to \( 4 \frac{1}{4} \), or 4.25)
4. \( 434 \) (which does not seem correct)

None of those options correctly represent \( A_9 = 18 \). If I interpret your responses correctly, perhaps each number is formatted differently than I expected.

If these are the only options available, none of them are correct, as \( A_9 \) should be \( 18 \). If there is a misunderstanding or if you need clarification, please let me know!

Answer 5

Given the explicit formula for the arithmetic sequence:

\[
A_n = \frac{1}{4} + (n - 1) \cdot \frac{1}{2}
\]

we need to find the 9th term (\( A_9 \)) by substituting \( n = 9 \) into the formula.

1. **Substituting \( n = 9 \)**:
\[
A_9 = \frac{1}{4} + (9 - 1) \cdot \frac{1}{2}
\]

2. **Calculate \( 9 - 1 \)**:
\[
9 - 1 = 8
\]

3. **Substituting this back into the equation**:
\[
A_9 = \frac{1}{4} + 8 \cdot \frac{1}{2}
\]

4. **Calculating \( 8 \cdot \frac{1}{2} \)**:
\[
8 \cdot \frac{1}{2} = 4
\]

5. **Now add \( \frac{1}{4} \) and \( 4 \)**:
\[
A_9 = \frac{1}{4} + 4 = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4}
\]

Now we can convert \( \frac{17}{4} \) into a mixed number:

\[
\frac{17}{4} = 4 \frac{1}{4}
\]

Now, we can look at your response options:

1. **\( 814 \)** (equivalent to \( 8 \frac{1}{4} \), or 8.25)
2. **\( 834 \)** (equivalent to \( 8 \frac{3}{4} \), or 8.75)
3. **\( 414 \)** (equivalent to \( 4 \frac{1}{4} \), or 4.25)
4. **\( 434 \)**

From our calculations, the correct answer is **\( 4 \frac{1}{4} \)**, which corresponds to **\( 414 \)**.

So, the correct response is \( 414 \).