a sum of money is shared amony nine people the first gets 75 the next 150 the next 225 and so on a how much many does the nineth people get b how much many is shared all together in maths
solving it pls
this is just an arithmetic sequence with
a = 75
d = 75
a_9 = a+8d
S9 = 9/2 (2a+9d)
So plug and chug
I want to join
I want to learn math on Ap and Gp
How much money is shared altogether ?-is it is 3,375
323
74646
To find the answers to your questions, let's break down the problem step-by-step:
1. Determine the pattern:
Looking at the scenario, we can observe that the amounts being received by each person are increasing by a fixed amount sequentially. In this case, the amounts are increasing by 75. So, we can conclude that it is an arithmetic sequence with a common difference of 75.
2. Find the nth term of the sequence:
The formula for finding the nth term of an arithmetic sequence is:
nth term = a + (n - 1) * d
where:
- nth term is the term we want to find,
- a is the first term of the sequence, and
- d is the common difference.
3. Calculate the ninth person's share:
Using the formula above, we can substitute the values as follows:
a = 75 (because the first person receives 75)
n = 9 (since we want to find the ninth term)
d = 75 (as mentioned, the common difference is 75)
Therefore, the ninth person's share is:
nth term = 75 + (9 - 1) * 75
= 75 + 8 * 75
= 75 + 600
= 675
So, the ninth person receives 675.
4. Calculate the total amount shared among all nine people:
Since the amounts are given in an arithmetic sequence, we can use the sum formula for an arithmetic series:
Sum = (n/2) * (2a + (n - 1) * d)
Using the formula, we can substitute the values as follows:
a = 75 (the first term)
n = 9 (the total number of terms)
d = 75 (the common difference)
Therefore, the total amount shared is:
Sum = (9/2) * (2 * 75 + (9 - 1) * 75)
= (9/2) * (150 + 8 * 75)
= (9/2) * (150 + 600)
= (9/2) * (750)
= 9/2 * 750
= 9 * 375
= 3375
So, a total amount of 3375 is shared among all nine people.