A sum of money is shared among eleven(11) people, so that the first get #75, the next #225, and so on.
(a) how much money does the eleventh person get
(b) how much is shared altogether
From what you have here, it seems that the preceding number is multiplied by 3. Looks like the 11th person gets a gigantic sum. I'll let you do the calculations.
or, the sequence is arithmetic, and grows by 150 for each person, so the 11th person gets 75 + 10*250 = 2575
S11 = 11/2 (75+2575) = _____
To find the answer to this question, we need to understand the pattern in which the money is being distributed and then apply that pattern to find the values for the eleventh person and the total amount shared.
The given pattern states that the first person receives #75, the second person receives #225, and so on. We can observe that the amount being received by each person is increasing by #150 each time.
(a) To find out how much money the eleventh person will receive, we can use the formula:
Amount received by n-th person = (n-1) * #150 + initial amount
In this case, the initial amount received by the first person is #75, so the eleventh person will receive:
Amount received by 11th person = (11 - 1) * #150 + #75
= 10 * #150 + #75
= #1500 + #75
= #1575
Therefore, the eleventh person will receive #1575.
(b) To find out the total amount shared among all 11 people, we can use the formula for the sum of an arithmetic series:
Sum = (n/2) * (first term + last term)
In this case, the first term is #75, and the last term is #1575 (the amount received by the eleventh person).
Sum = (11/2) * (#75 + #1575)
= (11/2) * #1650
= 5.5 * #1650
= #9075
Therefore, the total amount shared altogether is #9075.