If C is the midpoint of AB, then we can write:

\(k.3^n-3^n=3^{n+3}-k.3^n\)

\(2*k*3^n=3^n+3^{n+3}\)

\(2*k*3^n=3^n(1+3^3)\)

\(2*k=1+3^3\)

k=14


C

Cheers

3^n+3 -3^n
3^n(27-1)
k=26/2
k=13

k*3^n=3^n-k*3^n
3^n (k-1)=3^n (3^3-k)
k-1=27-1--→k=14

Carcass pls provide an explanation for this question, I am not getting the solutions above

The midpoint means that the segment AC=CB

Therefore our midpoint that is \(k*3^n\) is equal to AC and CB divided by two because is the midpoint we need to find out

\(k*3^n = \frac{(3^n + 3^{n+3})}{2}\)

At this point is just a matter of computation

K is = to 14

C is the answer

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