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Question: Find a1 for the given geometric series: Sn = 86185, r = 2, n = 10

To find a1 (the first term of the geometric series), we first have to understand the formula for the sum of the first n terms of a geometric series. This is given by Sn = a1 * (r^n-1) / (r-1). You have Sn = 86185, r = 2, and n = 10. Plugging these values into the formula, we can solve for a1. 86185 = a1 * (2^10 - 1) / (2 - 1) When you do the calculations, you first calculate the exponent (2^10 equals 1024), then subtract 1 from the result (1024-1 equals 1023), and divide 86185 by 1023, you get a1 (the first term) to be 84.22. Round it to two decimal places as per standard rounding rules. So, a1 is approximately 84.22.

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