Final Answer:
The first term of the arithmetic sequence is -2.
Step-by-step explanation:
In order to find the first term of the arithmetic sequence, the given information must be used. It is given that the first term equals the third minus the second and that the fourth term is 6. This means that the third term of the sequence is 8. Therefore, the equation for the first term of the sequence is a1 = 8 - 2. When this equation is solved, it is found that the first term of the sequence is -2.
To find the first term, the equation a1 = a3 - a2 is used. This equation states that the first term of an arithmetic sequence is equal to the third term minus the second term. Thus, the third term (a3) and the second term (a2) of the sequence must be known. In the given problem, it is given that the fourth term (a4) is 6 and the first term (a1) is the third term (a3) minus the second term (a2).
To solve the equation, the value of the third term (a3) must be found. This can be done by utilizing the given information. It is given that the fourth term is 6, which means that the third term must be 8. Therefore, the equation for the first term is a1 = 8 - 2. When this equation is solved, it is found that the first term of the sequence is -2.
To conclude, the first term of the arithmetic sequence is -2 and is found by utilizing the equation a1 = a3 - a2. In the given problem, it is given that the fourth term is 6, which means that the third term must be 8. Therefore, the equation for the first term is a1 = 8 - 2, and when solved, it is found that the first term of the sequence is -2.