Reported Question / Answer
To find twice the sum of the first fifteen terms of the series 5, 10, 20, ... , you can use the formula for the sum of a geometric series: Sum = a * (1 - r^n) / (1 - r) In this series: - a is the first term, which is 5. - r is the common ratio, which is 2 (since each term is double the previous one). - n is the number of terms, which is 15. Plug these values into the formula: Sum = 5 * (1 - 2^15) / (1 - 2) Now, calculate the sum: Sum = 5 * (1 - 32768) / (1 - 2) Sum = 5 * (-32767) / (-1) Sum = 5 * 32767 Sum = 163,835 So, the sum of the first fifteen terms of the series is 163,835, and twice that is: 2 * 163,835 = 327,670 Therefore, twice the sum of the first fifteen terms of the series is 327,670.
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