The required 8th term of a geometric progression is -0.75.
Given,
a4 = 12 and a5 = -6
The 8th term of the geometric progression is to be determined.
What is geometric progression?
Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
[tex]-6 = a_5\\-6 = ar^{4-1}\\-6 = ar^4[/tex] - - - - - ( 1 )
similarly,
[tex]-12 = a_4\\-12=ar^3[/tex] - - - - - - - (2)
Dividing equation 1 with 2
[tex]-6/-12 = r^4/r^3\\1/2 = r\\r = 1/2[/tex]
Put r in equation 2
-12 = a (1/2)³
-12*8 = a
a = -96
8th term,
[tex]a_8 = ar^7\\a_8 = -96 (1/2)^7\\a_8 = -0.75[/tex]
Thus, the required 8th term of a geometric progression is -0.75.
Learn more about geometric progression here: https://brainly.com/question/4853032
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