Find the following sum: 9 + 10 + 11 + ... + 87
Do you mean that the sum of those numbers EQUALS 87?
looks like an AS
a = 9 , d = 1 , n = ?
a + (n-1)d = 87
9 + (n-1) = 87
n = 87-8 = 79
sum(79) = (79/2)(first + last)
= (79/2)(9+87) = 3792
or
sum = sum(all of 87) - sum(all of 8)
= 87(88)/2 - 8(9)/2
= 3792
To find the sum of a consecutive sequence of numbers, we can use the arithmetic series formula. The formula for the sum of an arithmetic series is:
S = (n/2)(a + l)
Where:
S is the sum of the series
n is the number of terms in the series
a is the first term in the series
l is the last term in the series
In this case, we are asked to find the sum of the numbers from 9 to 87, where 9 is the first term and 87 is the last term.
First, let's find the number of terms in the series. We can do this by subtracting the first term from the last term and then adding 1:
n = (87 - 9) + 1
n = 79 + 1
n = 80
Now, we can plug these values into the formula to find the sum:
S = (80/2)(9 + 87)
S = (40)(96)
S = 3840
Therefore, the sum of the numbers from 9 to 87 is 3840.