Question 6

Explanation

Arithmetic Sequence Analysis

The pattern of temperature decrease in the table forms an arithmetic sequence. For every $100 \text{ m}$ increase in altitude, the temperature drops by $2^\circ\text{C}$.

Given:

• The first term ($U_1$) at an altitude of $100 \text{ m}$ is $32$.
• The common difference ($b$) is $-2$.

An altitude of $800 \text{ m}$ corresponds to the 8th term ($U_8$), and an altitude of $1200 \text{ m}$ corresponds to the 12th term ($U_{12}$).

The formula for the $n$-th term of an arithmetic sequence is:

So, the ratio of the air temperature at the two altitudes is:

Therefore, the temperature ratio is $9:5$.