A sum of money is shared among 9 people so that the first get 75 naira the next 150 naira the next 225 naira and so on , how much money is shared All together, how much money does the 9th person gets
The sum of money shared among the 9 people follows an arithmetic sequence. The common difference between each consecutive person's share is 75 naira.
To find the sum of the money shared by all 9 people, we can use the formula for the sum of an arithmetic sequence: Sn = (n/2)(a + l), where Sn represents the sum of the first n terms, a is the first term, and l is the last term.
In this case, we are given that the first term (a) is 75 naira and the ninth term (l) is 9 * 75 = 675 naira (since each term is 75 naira more than the previous term).
Using the formula, Sn = (n/2)(a + l), we can substitute the given values to solve for the sum of the money shared by all 9 people:
Sn = (9/2)(75 + 675)
= (9/2)(750)
= 9 * 375
= 3375 naira.
Therefore, the total sum of money shared among all 9 people is 3375 naira.
To find out how much money the 9th person receives, we can simply take the 9th term of the arithmetic sequence, which is 675 naira.
The amount the night person gets is 75×9=675naira.
The total money shared all together is 75+150+225+300+375+450+525+600+675=3375naira.
Apologies for the confusion in my previous response. Yes, you are correct.
The amount the 9th person receives is 675 naira.
The total sum of money shared among all 9 people is indeed 3375 naira.
Thank you for pointing out the error, and I apologize for any confusion caused.
To find the total amount of money shared among the 9 people, we need to find the sum of the arithmetic series.
The formula to find the sum of an arithmetic series is:
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.
Given:
First term, a = 75 naira
Common difference, d = 75 naira (since the amounts increase by 75 naira for each person)
Number of terms, n = 9
We can calculate the last term using the formula for the nth term of an arithmetic sequence:
l = a + (n - 1) * d
l = 75 + (9 - 1) * 75
l = 75 + 8 * 75
l = 75 + 600
l = 675 naira
Substituting the known values into the sum formula:
Sn = (n/2) * (a + l)
Sn = (9/2) * (75 + 675)
Sn = 4.5 * 750
Sn = 3375 naira
Therefore, the total amount of money shared among the 9 people is 3375 naira.
To find the amount the 9th person receives, we can use the formula for finding the nth term:
an = a + (n-1) * d
a9 = 75 + (9 - 1) * 75
a9 = 75 + 8 * 75
a9 = 75 + 600
a9 = 675 naira
Therefore, the 9th person receives 675 naira.