To find the sum of the first N terms of a geometric sequence, we can use the formula:
Sn = a * (1 - r^N) / (1 - r)
where Sn is the sum of the first N terms, a is the first term, r is the common ratio, and N is the number of terms.
In this case, a = 3 and r = 2. Let’s find the sum of the first N terms:
Sn = 3 * (1 - 2^N) / (1 - 2)
Simplifying the formula:
Sn = 3 * (1 - 2^N) / (-1)
Sn = -3 * (1 - 2^N)
So, the sum of the first N terms of the given geometric sequence is -3 * (1 - 2^N).
To find the common ratio, we can use the formula:
r = (G2 / G1)
where G1 is the first term and G2 is the second term.
In this case, G1 = 3 and r = 2. Let’s find the second term:
G2 = G1 * r
G2 = 3 * 2
G2 = 6
So, the common ratio of the given geometric sequence is 2.
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