Final answer:
The student's question is about finding the value of N for the sum of a geometric series. We must use the formula for the sum of a geometric series and algebra to solve for N when the sum is 6560.
Step-by-step explanation:
The student is asking for the value of N in a geometric series when the sum of the first N terms equals 6560. The series given is 2 + 6 + 18 + 54 + ..., which is a geometric progression where each term after the first is multiplied by the common ratio of 3. To find the sum of such a series, we can use the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r)
where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms. Plugging the given values into the formula and solving for N requires algebraic manipulation. Since the calculation process and exact algebraic solution is not provided in the information box, we would need to carry out the steps of solving the equation ourselves.