The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive?
Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
think of an arithmetic sequence where
a=60 and d=1. The sum of the 1st 21 terms is thus
21/2(2*60+20*1) = 1470
or, since each number is 20 more than the terms of the first sequence, add 21*20 = 400, to get 1470
To find the sum of consecutive integers, you can use the formula for the sum of an arithmetic series. The formula is:
Sum = (n/2) * (first term + last term)
To apply this formula to the given scenario, let's find the sum of the integers from 40 to 60, inclusive.
First, we need to determine the number of terms in this series. Since we are going from 40 to 60, inclusive, the number of terms is (60 - 40 + 1) = 21.
Next, we find the first term and the last term. The first term is 40, and the last term is 60.
Now, we can plug in these values into the sum formula:
Sum = (21/2) * (40 + 60)
Simplifying this equation gives:
Sum = 10.5 * 100
Sum = 1050
So, the sum of the integers from 40 to 60, inclusive, is indeed 1050.
Now, let's find the sum of the integers from 60 to 80, inclusive, using the same pattern.
Again, we need to determine the number of terms. The number of terms is (80 - 60 + 1) = 21.
Now, we find the first term and the last term. The first term is 60, and the last term is 80.
Using the sum formula:
Sum = (21/2) * (60 + 80)
Simplifying this equation gives:
Sum = 10.5 * 140
Sum = 1470
Therefore, the sum of the integers from 60 to 80, inclusive, is 1470.