PLEASE help me with this algebra II question! #5 please!

is a geometric sequence, which means consecutive terms occur in a fixed ratio. In other words,

for some fixed number .

Using this rule, we have

So, given that and , we have

We can write in terms of :

(notice how the subscript and exponent add up to ) so the sequence is given by the explicit rule

Incidentally, we can pull out the first term from this sequence by plugging in to find .

Next, if denotes the th partial sum of the sequence, then

For geometric sequences, we can replace through with terms containing :

Multiply both sides by :

Subtract from ; a bunch of terms cancel and we're left with

For the sequence at hand, plug in and . Then

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step-by-step explanation: