Question
What is the sum of the geometric series 14+70+350+......+43750
Answers
GPT 3.5
The geometric series can be written as 14 + 14*5 + 14*5^2 + ... + 14*5^6, where the common ratio is 5 and the first term is 14.
The formula for the sum of a geometric series is S = a * (r^n - 1) / (r - 1), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.
Using this formula:
S = 14 * (5^7 - 1) / (5 - 1)
S = 14 * (78125 - 1) / 4
S = 14 * 78124 / 4
S = 1367186
Therefore, the sum of the geometric series is 1,367,186.
The formula for the sum of a geometric series is S = a * (r^n - 1) / (r - 1), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.
Using this formula:
S = 14 * (5^7 - 1) / (5 - 1)
S = 14 * (78125 - 1) / 4
S = 14 * 78124 / 4
S = 1367186
Therefore, the sum of the geometric series is 1,367,186.