Question

find the 11th term of the arithmetic sequence graphed below.

Explanation:

Step1: Identify points from graph

From the graph, let's assume the points (n, \(a_n\)) are: when \(n = 1\), \(a_1=-15\); \(n = 2\), \(a_2=-9\); \(n = 3\), \(a_3=-3\); \(n = 4\), \(a_4=3\) (checking the pattern, common difference \(d\) is \(a_2 - a_1=-9 - (-15)=6\), \(a_3 - a_2=-3 - (-9)=6\), so \(d = 6\)).

Step2: Arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\). Here, \(a_1=-15\), \(d = 6\), \(n = 11\).

Step3: Substitute values

Substitute into the formula: \(a_{11}=-15+(11 - 1)\times6\)
\(a_{11}=-15 + 10\times6\)
\(a_{11}=-15 + 60\)
\(a_{11}=45\)

Answer:

45