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

434
4 Start Fraction 3 over 4 End Fraction

414
4 Start Fraction 1 over 4 End Fraction

834
8 Start Fraction 3 over 4 End Fraction

814

1 answer

To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = 14 + (n - 1) \cdot 12 \), we will substitute \( n = 9 \) into the formula.

The formula is:

\[ A_n = 14 + (n - 1) \cdot 12 \]

For \( n = 9 \):

\[ A_9 = 14 + (9 - 1) \cdot 12 \] \[ A_9 = 14 + 8 \cdot 12 \] \[ A_9 = 14 + 96 \] \[ A_9 = 110 \]

Now, let's consider the responses given:

  • 434
  • \( 4 \frac{3}{4} \)
  • 414
  • \( 4 \frac{1}{4} \)
  • 834
  • \( 8 \frac{3}{4} \)
  • 814

None of these options match the calculated value of \( 110 \). Please verify if the formula or the responses are correct as provided.