Question

Which of the following correctly uses the explicit formula An=1/4+(n-1)•2, To find the 9th term of the described arithmetic sequence.
the correct answer to this question I was given was 4 1⁄4 I don't know how that's the answer Explain

Answer 1

No my Math teacher said that the correct answer was 4 1⁄4 I don't understand how she got that Help. Because the answer you provided I can't put Or pick

Answer 2

All right she must have put the wrong formula or something, I don't know. Thanks for your help :)

Answer 3

To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = \frac{1}{4} + (n-1) \cdot 2 \), we need to substitute \( n = 9 \) into the formula.

Here's how to do it step by step:

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

2. **Calculate \( 9 - 1 \)**:
\[
9 - 1 = 8
\]
So, we can rewrite the equation as:
\[
A_9 = \frac{1}{4} + 8 \cdot 2
\]

3. **Calculate \( 8 \cdot 2 \)**:
\[
8 \cdot 2 = 16
\]
Now we have:
\[
A_9 = \frac{1}{4} + 16
\]

4. **Convert 16 to a fraction to combine with \( \frac{1}{4} \)**:
\[
16 = \frac{64}{4}
\]
So we can rewrite \( A_9 \) as:
\[
A_9 = \frac{1}{4} + \frac{64}{4}
\]

5. **Combine the fractions**:
\[
A_9 = \frac{1 + 64}{4} = \frac{65}{4}
\]

6. **Convert \( \frac{65}{4} \) to a mixed number**:
\[
\frac{65}{4} = 16 \frac{1}{4}
\]

However, it seems there was confusion in your mention of \( 4 \frac{1}{4} \); the correct answer for \( A_9 \) is \( 16 \frac{1}{4} \) or \( 16.25 \) depending on how you want to express the answer.

So the correct answer for the 9th term using the formula is **16.25** or **16 \frac{1}{4}**. If you were told it's \( 4 \frac{1}{4} \), that appears to be incorrect for this calculation.

Answer 4

If your teacher indicated that the 9th term is \( 4 \frac{1}{4} \), it suggests that there might have been a misunderstanding about the term number or the formula being used. Let's carefully work through the formula step-by-step again:

The formula you provided is:
\[
A_n = \frac{1}{4} + (n-1) \cdot 2
\]

To find the 9th term (\( n = 9 \)), substitute \( n \) with \( 9 \):

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

2. Calculate \( 9 - 1 \):
\[
9 - 1 = 8
\]
So now we have:
\[
A_9 = \frac{1}{4} + 8 \cdot 2
\]

3. Calculate \( 8 \cdot 2 \):
\[
8 \cdot 2 = 16
\]
Now the equation looks like:
\[
A_9 = \frac{1}{4} + 16
\]

4. Convert \( 16 \) to a fraction with the same denominator for easy addition:
\[
16 = \frac{64}{4}
\]
Now we can write:
\[
A_9 = \frac{1}{4} + \frac{64}{4} = \frac{1 + 64}{4} = \frac{65}{4}
\]

5. To convert \( \frac{65}{4} \) to a mixed number:
\[
\frac{65}{4} = 16 \frac{1}{4} \quad \text{(this equals 16.25 as a decimal)}
\]

### Conclusion
Thus, following the formula correctly shows that \( A_9 = 16 \frac{1}{4} \).

**Possible Explanation for \( 4 \frac{1}{4} \)**:
- **Miscommunication**: It’s possible that there was a misunderstanding regarding which term was being calculated.
- **Different Formula**: Ensure that the exact formula your teacher intended was used.

If your teacher still insists the answer is \( 4 \frac{1}{4} \), I recommend discussing your calculations with her directly to clarify any confusion.

Answer 5

You're welcome! It's definitely possible that there was a mix-up with the formula. If you have any more questions about arithmetic sequences or any other math topic, feel free to ask. Good luck, and I'm glad I could help! 😊