Analyze the explicit formula of the arithmetic sequence an=3.7+1/2n

Question

and report the ninth term, rounded to the nearest tenth.(1 point)
Responses

an=4.2
a subscript n baseline equals 4.2

a9=8.2
a subscript 9 baseline equals 8.2

a9=10.6
a subscript 9 baseline equals 10.6

a9=8

Answer 1

To find the ninth term \( a_9 \) of the arithmetic sequence given by the formula:

\[ a_n = 3.7 + \frac{1}{2} n \]

we will substitute \( n = 9 \) into the formula.

\[ a_9 = 3.7 + \frac{1}{2} \cdot 9 \]

Calculating \( \frac{1}{2} \cdot 9 \):

\[ \frac{1}{2} \cdot 9 = 4.5 \]

Now substituting back into the formula:

\[ a_9 = 3.7 + 4.5 = 8.2 \]

Therefore, the ninth term \( a_9 \), rounded to the nearest tenth, is:

\[ \boxed{8.2} \]