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.
Use the Gauss method:
60+61+62...+70+71...+80
80+79+78+..+70+69...+60
Add the two lines, you will get the sum 140 21 times. So half the sum is 70*21=1470.
To find the sum of consecutive integers, you can use the formula for the sum of an arithmetic series:
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.
In this case, the first term (a) is 40, and the last term (l) is 60. The number of terms (n) can be calculated as (l - a + 1).
n = l - a + 1
= 60 - 40 + 1
= 21
Using the formula for the sum of an arithmetic series, we can find the sum of the integers from 40 to 60:
Sn = (n/2)(a + l)
= (21/2)(40 + 60)
= 10.5(100)
= 1050
Therefore, the sum of the integers from 40 to 60 inclusive is 1050.
To find the sum of the integers from 60 to 80 inclusive, we can use the same formula. The first term (a) is 60 and the last term (l) is 80. The number of terms (n) can be calculated as (l - a + 1).
n = l - a + 1
= 80 - 60 + 1
= 21
Using the formula for the sum of an arithmetic series, we can find the sum of the integers from 60 to 80:
Sn = (n/2)(a + l)
= (21/2)(60 + 80)
= 10.5(140)
= 1470
Therefore, the sum of the integers from 60 to 80 inclusive is 1470.
To find the sum of a consecutive sequence of numbers, you can use the formula for the sum of an arithmetic series. The formula is given by:
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.
In this case, the first term (a) is 40, and the last term (l) is 60. We can calculate the number of terms (n) using the formula:
n = l - a + 1
Therefore, n = 60 - 40 + 1 = 21.
Now, we have all the values we need to find the sum of the series:
Sn = (n/2)(a + l)
= (21/2)(40 + 60)
= (21/2)(100)
= 21 * 50
= 1050
So, the sum of the integers from 40 to 60, inclusive, is indeed 1050.
To find the sum of the integers from 60 to 80, inclusive, we can use the same approach:
The first term (a) is 60, and the last term (l) is 80. The number of terms (n) is given by:
n = l - a + 1
= 80 - 60 + 1
= 21
Using the formula for the sum of the series, we have:
Sn = (n/2)(a + l)
= (21/2)(60 + 80)
= (21/2)(140)
= 21 * 70
= 1470
Therefore, the sum of the integers from 60 to 80, inclusive, is 1470.