Question

Consider this series.

2+6+18+54+...
If the sum of the first n terms of the series is 6,560, what is the value of n?
A. n=10
B. n=9
C. n=7
D. n=8

Answer 1

The problem is a geometric series where each term is triple the previous one. By applying the sum formula for a geometric series, the value of n when the sum of the first n terms is 6,560 is found to be 8.

Step-by-step explanation:

The question presented is a mathematical problem involving a geometric series. To find the value of n for which the sum of the first n terms is 6,560, one must understand the formula for the sum of a geometric series. The series given is 2 + 6 + 18 + 54 + ..., where each term is three times the previous term, indicating a common ratio of 3. The first term (a) is 2, and the common ratio (r) is 3. Using the sum formula for geometric series:

• Sn = a(1-rn)/(1-r) where Sn is the sum of the first n terms,

We plug in the values: 6,560 = 2(1-3n)/(1-3). Solving for n, we find that n is 8. Therefore, the correct answer is D. n=8.