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Explanation:
r = common ratio
To get any term in a geometric sequence, we multiply the previous term by r.
So that means 4r is the second term, since 4 is the first term.
The third term is (4r)*r = 4r^2, which is equal to 9 as given to us.
4r^2 = 9
4r^2 - 9 = 0
(2r)^2 - (3)^2 = 0
(2r - 3)(2r + 3) = 0 ... difference of squares rule
2r-3 = 0 or 2r+3 = 0
2r = 3 or 2r = -3
r = 3/2 or r = -3/2
r = 1.5 or r = -1.5
We can use each r value to find the possible second term
S = 4r = 4*(1.5) = 6
S = 4r = 4*(-1.5) = -6
The second term is either 6 or -6.
We could have this sequence: 4, 6, 9, ...
Or we could have this sequence: 4, -6, 9, ...
The possible values of the missing term in the geometric sequence should be considered as the 6 or -6.
Since
r = common ratio
For get any term in a geometric sequence, we have to multiply the previous term by r.
Here first term is 4 so the second term be 4r
And, the third term be [tex](4r)*r = 4r^2[/tex] , that is equivalent to 9
[tex]4r^2 = 9\\\\4r^2 - 9 = 0\\\\(2r)^2 - (3)^2 = 0[/tex]
(2r - 3)(2r + 3) = 0
2r-3 = 0
or
2r+3 = 0
2r = 3 or 2r = -3
[tex]r = 3/2\ or\ r = -3/2[/tex]
r = 1.5 or r = -1.5
Now
S = 4r = 4(1.5) = 6
S = 4r = 4(-1.5) = -6
Hence, The possible values of the missing term in the geometric sequence should be considered as the 6 or -6.
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