What is the sum of the geometric series Capital sigma, subscript n equals 1, superscript 10, baseline 6 times 2 superscript n.?
(1 point)
Responses
15,658
15,658
6,138
6,138
12,276
12,276
756
The sum of the geometric series Σn=1^10 6 x 2^n is 15,658.
Calculating each term:
1st term: 6 x 2^1 = 12
2nd term: 6 x 2^2 = 24
3rd term: 6 x 2^3 = 48
4th term: 6 x 2^4 = 96
5th term: 6 x 2^5 = 192
6th term: 6 x 2^6 = 384
7th term: 6 x 2^7 = 768
8th term: 6 x 2^8 = 1536
9th term: 6 x 2^9 = 3072
10th term: 6 x 2^10 = 6144
Adding all these terms together: 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072 + 6144 = 15,658.
Therefore, the correct answer is 15,658.