Question
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
(1 point)
Responses
15,658
15,658
6,138
6,138
12,276
12,276
756
Answers
GPT 3.5
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.
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.