Question

Which of the following correctly uses the explicit formula, An=14+(n−1)⋅12
, to find the 9th term of the described arithmetic sequence?(1 point)
Responses

4 3/4
4 Start Fraction 3 over 4 End Fraction

4 1/4
4 Start Fraction 1 over 4 End Fraction

8 1/4
8 Start Fraction 1 over 4 End Fraction

8 3/4

Answers

Answer
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

434
4 Start Fraction 3 over 4 End Fraction

414
4 Start Fraction 1 over 4 End Fraction

814
8 Start Fraction 1 over 4 End Fraction

8 3/4
Answered by GPT-4o mini
To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = 14 + (n - 1) \cdot 12 \), we need to substitute \( n = 9 \) into the formula:

\[
A_9 = 14 + (9 - 1) \cdot 12
\]

Now, calculate:

1. Substitute \( n - 1 \):
\[
A_9 = 14 + (8) \cdot 12
\]

2. Multiply:
\[
A_9 = 14 + 96
\]

3. Add:
\[
A_9 = 110
\]

Thus, the 9th term \( A_9 \) is 110. It seems none of the provided options match this result. If you're looking for a mistake or a revision of the provided answer options, please verify the options or the formula correct.
Answered by GPT-4o mini
To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = \frac{1}{4} + (n - 1) \cdot \frac{1}{2} \), we will substitute \( n = 9 \) into the formula:

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

Now, calculate step by step:

1. Calculate \( n - 1 \):
\[
A_9 = \frac{1}{4} + (8) \cdot \frac{1}{2}
\]

2. Multiply:
\[
A_9 = \frac{1}{4} + 4
\]

3. Convert \( 4 \) to quarters:
\[
4 = \frac{16}{4}
\]

4. Add:
\[
A_9 = \frac{1}{4} + \frac{16}{4} = \frac{17}{4}
\]

Now, to express \( \frac{17}{4} \) as a mixed number:

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

Thus, the 9th term \( A_9 \) is \( 4 \frac{1}{4} \).

The correct response is:

**4 Start Fraction 1 over 4 End Fraction**.

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