Ask AI: Find the sum of the arithmetic series: 27 + 54 + 81 + 108 + ... + 540

The sum of an arithmetic series can be calculated using the formula: S = n/2 * (a + l) where: - S is the sum of the series - n is the number of terms - a is the first term - l is the last term In your case, the first term (a) is 27, the last term (l) is 540, and the common difference (d) is 54 - 27 = 27. To find the number of terms (n), use the formula for an arithmetic sequence: l = a + (n - 1) * d. Let's solve for n: 540 = 27 + (n - 1) * 27. After simplification, we find: n - 1 = (540 - 27) / 27 = 19. So, n = 19 + 1 = 20. Now we can substitute a, l, and n into the formula for the sum of an arithmetic series: S = 20 / 2 * (27 + 540) S = 10 * 567 = 5670. So, the sum of the series 27 + 54 + 81 + 108 + ... + 540 is 5670.