The fourth term in the sequence, with the following definition in which the value of the first term is 0, is -42.
What is geometric sequence?
Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
The sequence given as,
[tex]a_{1} = 0\\a_{n} = 2(a_{n-1} -3)[/tex]
In this expression, n represent the number of term. The first term is zero. Thus, the second term of the sequence is,
[tex]a_{2} = 2(a_{2-1} -3)\\a_{2} = 2(a_{1} -3)\\a_{2} = 2(0 -3)\\a_{2} = -6[/tex]
Third term is,
[tex]a_{3} = 2(a_{3-1} -3)\\a_{3} = 2(a_{2} -3)\\a_{3} = 2(-6 -3)\\a_{3} = -18[/tex]
Similarly, the fourth term is,
[tex]a_{4} = 2(-18 -3)\\a_{2} = -42[/tex]
Hence, the fourth term in the sequence with the following definition in which the value of the first term is 0, is -42.
Learn more about the geometric sequence here;
https://brainly.com/question/1509142
