Question

Analyze the explicit formula of the arithmetic sequence an = 3.7 + ⅔n and report the ninth term, rounded to the nearest tenth. (1 point)
0 ag = 8
0 ag = 8.2
0 ag = 10.6
0 an = 4.2

Answer 1

To analyze the explicit formula of the arithmetic sequence given by \( a_n = 3.7 + \frac{2}{3}n \), we need to find the ninth term, \( a_9 \).

We can substitute \( n = 9 \) into the formula:

\[
a_9 = 3.7 + \frac{2}{3} \cdot 9
\]

Calculating \( \frac{2}{3} \cdot 9 \):

\[
\frac{2}{3} \cdot 9 = 6
\]

Now, substitute back into the equation for \( a_9 \):

\[
a_9 = 3.7 + 6 = 9.7
\]

Now we need to round 9.7 to the nearest tenth, which is still 9.7. However, the options provided do not include 9.7.

If we check the options given:
- 0 ag = 8
- 0 ag = 8.2
- 0 ag = 10.6
- 0 an = 4.2

None of these match with the calculated term \( a_9 = 9.7 \). Hence, it seems like there may have been a misunderstanding in the options. The calculation yields \( a_9 = 9.7 \), rounded to the nearest tenth.