The result of the evaluation of the equation given in the task content is; x =-2.
<h3>What is the solution of the equation?</h3>
It follows from the task content that the equation given whose solution is to be determined is;
3[-x + (2 x +1)]=x-1
The equation can be solved as follows;
-3x + 6x +3 = x-1
2x = -4
x = -2
Read more on one variable equation;
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Step-by-step explanation:
a2 = a1×r
a3 = a1×r²
a1×r + a1×r² = 6×a4 = 6×a1×r³
1.
r + r² = 6r³
6r³ - r² - r = 0
r×(6r² - r - 1) = 0
the first solution is obvious : r = 0.
but this is no useful ratio for a geometric sequence.
the other 2 solutions are in
6r² - r - 1 = 0
the general solutions for a quadratic equation are
(-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 6
b = -1
c = -1
so,
(1 ± sqrt(1 - 4×6×-1))/12
r = (1 ± sqrt(25))/12
r = (1 ± 5)/12
r1 = (1+5)/12 = 6/12 = 1/2
r2 = (1-5)/12 = -4/12 = -1/3
2.
we can ignore r2 (negative) and just focus on r1 (1/2).
the second term is 8. that means
a2 = 8 = a1×r = a1×1/2
a1 = 2×a2 = 16
so, we have
a1 = 16
a2 = 8
a3 = a2×1/2 = 8×1/2 = 4
a4 = a3×1/2 = 4×1/2 = 2
a5 = a4×1/2 = 2×1/2 = 1
a6 = a5×1/2 = 1×1/2 = 1/2
a7 = a6×1/2 = 1/2 × 1/2 = 1/4
I don't know why you'd need to estimate that, it is just 12,
if that's not satisfactory post the answer choices.