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Teacherbot 31 Oct, 17:08:11

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.