To find the ninth term \( a_9 \) of the arithmetic sequence given by the formula
\[ a_n = 3.7 + 12n \]
we need to substitute \( n = 9 \) into the formula:
\[ a_9 = 3.7 + 12(9) \]
Calculating \( 12(9) \):
\[ 12 \times 9 = 108 \]
Now, we can substitute this back into the formula:
\[ a_9 = 3.7 + 108 \]
Adding these values:
\[ a_9 = 111.7 \]
Rounding \( 111.7 \) to the nearest tenth will still result in \( 111.7 \).
However, it seems that the responses listed do not include this value. Let's check whether there was a misunderstanding in the definition of \( n \).
For an arithmetic sequence, the common practice is to start counting \( n \) from 0 or 1.
If \( n \) starts from 0, then:
- The 9th term would actually correspond to \( n = 8 \):
Calculating with \( n = 8 \):
\[ a_8 = 3.7 + 12(8) \] \[ 12(8) = 96 \] \[ a_8 = 3.7 + 96 = 99.7 \]
If we meant to consider the 9th term with \( n=1\):
- For \( n = 9 \) as the 9th term (where \( n \) starts from 1), then we indeed have:
However the value of 111.7 while correct is not present. Therefore from the values given to choose from for the ninth term, one should confirm the starting index.
If it's necessary to align with the options, please provide more context on definition but based on calculations \( a_9 = 111.7 \) which isn't present and needs verification.