Question

A geometric sequence has a first term 3 and a common ratio of 2. Determine the partial sum of the first 10 terms. Answers:

(A) -3,069
(B) 3,069
(C) 59,048
(D) 1,536

Answer 1

(A) -3,069. The partial sum of the first 10 terms of the given geometric sequence is -3,072.

Step-by-step explanation:

To find the partial sum of the first 10 terms of a geometric sequence with a first term of 3 and a common ratio of 2, we can use the formula for the sum of a geometric series: Sn = a(1 - r^n)/(1 - r), where Sn is the sum, a is the first term, r is the common ratio, and n is the number of terms.

Plugging in the given values, we have Sn = 3(1 - 2^10)/(1 - 2). Simplifying this expression gives us Sn = 3(1 - 1024)/(-1), which is equal to 3072/(-1) = -3,072.

Therefore, the partial sum of the first 10 terms of the given geometric sequence is -3,072.