To find the sum of all integers between 100 and 1000 that are divisible by 7, we can use the formula for the sum of an arithmetic series.
The first term (\(a\)) is the smallest number in the range that is divisible by 7, which is 105. The last term (\(l\)) is the largest number in the range that is divisible by 7, which is 994. The common difference (\(d\)) is 7.
The formula for the sum (\(S\)) of an arithmetic series is given by:
\[ S = \frac{n}{2} \times (a + l) \]
where \(n\) is the number of terms.
First, let's find the number of terms (\(n\)):
\[ n = \frac{l - a}{d} + 1 \]
\[ n = \frac{994 - 105}{7} + 1 \]
\[ n = \frac{889}{7} + 1 \]
\[ n = 127 \]
Now, plug the values into the sum formula:
\[ S = \frac{127}{2} \times (105 + 994) \]
\[ S = \frac{127}{2} \times 1099 \]
\[ S = \frac{127 \times 1099}{2} \]
\[ S = 69373.5 \]
So, the sum of all integers between 100 and 1000 that are divisible by 7 is 69373.5.
0 टिप्पणियाँ:
Post a Comment