The first three-term of the geometric progression is 120, -60, and 30.
Given that,
The geometric sequence has a1= 120 and whose common ratio is r = -1/2. First, three terms of the geometric sequence are to be determined.
What is geometric progression?
Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
The nth term of the geometric progression is given by,
[tex]a_n= ar^{n-1}\\[/tex]
Since,
For the first term three-term of the geometric progression.
[tex]a_1 = 120[/tex] are r = -1/2 is given
Let the first three-term of the geometric progression is [tex]120, a_2, a_3[/tex].
For the second term of the sequence n = 2
[tex]a_2 = ar^{2-1}\\a_2 = 120 (-1/2)^1\\a_2 = -60[/tex]
For the third term of the sequence,
n = 3
[tex]a_3=120(-1/2)^{3-1}\\a_3 = 120 * 1/4\\a_3 = 30[/tex]
Thus the first three-term of the geometric progression is 120, -60, 30.
Learn more about geometric progression here: https://brainly.com/question/4853032
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