Question

Consider this geometric series. 4+12+36+108+... The sum of the first n terms in the series is 4,372.

a) n=3
b) n=4
c) n=5
d) n=6

Answer 1

The question is about finding the value of n for which the sum of the first n terms of a geometric series equals 4,372. The series has a common ratio of 3, starting with the term 4. By applying the formula for the sum of a geometric series, one can calculate the correct number of terms.

Step-by-step explanation:

The student is asking about a geometric series with a sum of the first n terms equal to 4,372. In this series, each term after the first is obtained by multiplying the preceding term by 3 (e.g., 4, 12, 36, ...). The formula for the sum of the first n terms of a geometric series is S_n = a(1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms. In this case, a = 4 and r = 3. Plugging in the values and solving for n will determine which of the options (a) n=3, (b) n=4, (c) n=5, or (d) n=6 is correct.