Question

40, 31, 22, ……
use the formula to determine the
32nd term

Explanation:

Step1: Identify the sequence type

The sequence is \(40, 31, 22, \dots\). The common difference \(d\) is \(31 - 40=-9\) and \(22 - 31 = -9\), so it's an arithmetic sequence. The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\), where \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.

Step2: Identify \(a_1\), \(d\), and \(n\)

Here, \(a_1 = 40\), \(d=-9\), and \(n = 32\).

Step3: Substitute into the formula

Substitute the values into \(a_n=a_1+(n - 1)d\):
\(a_{32}=40+(32 - 1)\times(-9)\)
First, calculate \(32 - 1 = 31\). Then, \(31\times(-9)=-279\). Then, \(40+(-279)=40 - 279=-239\).

Answer:

\(-239\)