A sum of money was shared among nine people so that the first get 75 the second 150 and so on
A. How much money does the ninth get
B. How much money was shared altogether
A. To find out how much money the ninth person gets, we can use the formula for an arithmetic series: nth term = a + (n-1)d, where a is the first term, n is the number of terms, and d is the common difference.
In this case, a = 75 (amount the first person gets), n = 9 (number of people), and d = 75 (difference between each person's share).
9th term = 75 + (9-1) * 75
9th term = 75 + 8 * 75
9th term = 75 + 600
9th term = 675
The ninth person gets 675.
B. To find out how much money was shared altogether, we can use the formula for the sum of an arithmetic series: Sn = n/2 * (a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
In this case, a = 75 (amount the first person gets), l = 675 (amount the ninth person gets), and n = 9 (number of people).
Sum = 9/2 * (75 + 675)
Sum = 4.5 * 750
Sum = 3375
Altogether, 3375 was shared among the nine people.