Maria is a singer who recently published her first album. She finds that the number of downloads of her album each month is three times the number of downloads the previous month. Maria’s album was downloaded 18 times the first month, 54 times the second month, 162 times the third month, and so on. If this pattern continues, how many times will Maria’s album have been downloaded in total after 7 months?
The number of downloads each month follows a geometric sequence, where the common ratio is 3. This means that each term is found by multiplying the previous term by 3.
The first term is 18, and the second term is 54, so the third term is 54 * 3 = <<54*3=162>>162.
Therefore, the number of downloads for each month can be calculated by 18 * 3^(n-1), where n is the month number.
The number of downloads after 7 months can then be calculated by adding up the total number of downloads for each month from month 1 to month 7.
Taking n = 7, the number of downloads for each month is 18 * 3^(7-1) = 18 * 3^6 = 18 * 729 = <<18*729=13122>>13,122.
To find the total number of downloads over 7 months, we can use the formula for the sum of a geometric series. The sum of a geometric series is given by S = a * (r^n - 1) / (r - 1), where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 18, r = 3, and n = 7.
The total number of downloads after 7 months is S = 18 * (3^7 - 1) / (3 - 1) = 18 * (2187 - 1) / 2 = 18 * 2186 / 2 = 19,674.
Therefore, Maria's album will have been downloaded a total of 19,674 times after 7 months. Answer: \boxed{19,674}.