Question

1. this graph represents an arithmetic sequence. what is the value of the first term in the sequence? options: $a_1 = 8$, $a_1 = 10$, $a_1 = -12$, $a_1 = -1$

Explanation:

Step1: Identify the first term's position

In an arithmetic sequence graph, the first term \(a_1\) corresponds to the point where \(n = 1\) (the first term's index). We analyze the graph's points.

Step2: Analyze the graph's coordinates

Looking at the graph, the lowest (first - in terms of sequence order, as \(n = 1\)) plotted point (the starting point of the sequence's graph) has a y - value (which represents the term value \(a_n\)) of \(- 12\)? Wait, no, let's re - examine. Wait, maybe I made a mistake. Wait, let's check the options again. Wait, the first term is when \(n = 1\). Let's look at the graph: the left - most (first) dot: let's count the grid. The y - axis: from - 10, the first dot is at \(y=- 12\)? No, wait the options: \(a_1=-12\) is an option. Wait, let's check the graph again. The first point (for \(n = 1\)): looking at the vertical (y) axis, the first dot is at \(y=-12\)? Wait, no, maybe I miscounted. Wait, the options are \(a_1 = 8\), \(a_1=10\), \(a_1=-12\), \(a_1 = - 1\). Wait, let's think about the arithmetic sequence graph. The first term is the value when \(n = 1\). From the graph, the first plotted point (the bottom - most, left - most) is at \(y=-12\)? Wait, no, maybe I made a mistake. Wait, let's check the coordinates. Let's assume the x - axis is the term number \(n\) and y - axis is \(a_n\). The first point (n = 1) has a y - value of \(-12\)? Wait, no, the options: \(a_1=-12\) is one of the options. Wait, but let's re - check. Wait, maybe the first term is when \(n = 1\), and the graph's first point (the starting point) is at \(y=-12\). So among the options, \(a_1=-12\) is the correct one? Wait, no, wait the options: \(a_1=-12\) is option C (assuming the options are labeled as A: \(a_1 = 8\), B: \(a_1=10\), C: \(a_1=-12\), D: \(a_1=-1\)). Wait, maybe I made a mistake in the initial analysis. Wait, let's re - examine the graph. The first dot (for \(n = 1\)): let's count the grid. The y - axis: from - 10, moving down 2 units (since each grid is 1 unit), so the y - value is \(-12\). So the first term \(a_1=-12\).

Answer:

\(a_1=-12\) (the option with \(a_1=-12\))