Question
Formulas for Sequences Quick Check
5 of 55 of 5 Items
Question
Which of the following correctly uses the explicit formula, An=14+(nā1)ā 12
, to find the 9th term of the described arithmetic sequence?(1 point)
Responses
434
4 Start Fraction 3 over 4 End Fraction
834
8 Start Fraction 3 over 4 End Fraction
414
4 Start Fraction 1 over 4 End Fraction
814
5 of 55 of 5 Items
Question
Which of the following correctly uses the explicit formula, An=14+(nā1)ā 12
, to find the 9th term of the described arithmetic sequence?(1 point)
Responses
434
4 Start Fraction 3 over 4 End Fraction
834
8 Start Fraction 3 over 4 End Fraction
414
4 Start Fraction 1 over 4 End Fraction
814
Answers
GPT-4o mini
To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = 14 + (n - 1) \cdot 12 \), you need to substitute \( n = 9 \) into the formula.
Starting with the formula:
\[
A_n = 14 + (n - 1) \cdot 12
\]
Substituting \( n = 9 \):
\[
A_9 = 14 + (9 - 1) \cdot 12
\]
Now calculate \( (9 - 1) \):
\[
A_9 = 14 + 8 \cdot 12
\]
Now, calculate \( 8 \cdot 12 \):
\[
A_9 = 14 + 96
\]
Finally, add 14 and 96:
\[
A_9 = 110
\]
So the 9th term of the sequence is \( 110 \).
However, it looks like \( 110 \) isn't one of the provided answers. Please double-check the options or the formula in case there's any misunderstanding or typographical error.
Starting with the formula:
\[
A_n = 14 + (n - 1) \cdot 12
\]
Substituting \( n = 9 \):
\[
A_9 = 14 + (9 - 1) \cdot 12
\]
Now calculate \( (9 - 1) \):
\[
A_9 = 14 + 8 \cdot 12
\]
Now, calculate \( 8 \cdot 12 \):
\[
A_9 = 14 + 96
\]
Finally, add 14 and 96:
\[
A_9 = 110
\]
So the 9th term of the sequence is \( 110 \).
However, it looks like \( 110 \) isn't one of the provided answers. Please double-check the options or the formula in case there's any misunderstanding or typographical error.