Sequence and Series: Find the sum of all integers between 84 and 719 which are exactly divisible by 5.
To find the sum of all integers between 84 and 719 that are divisible by 5, we first need to determine the first and last terms in the sequence.
The first term divisible by 5 greater than or equal to 84 is 85 (85 divided by 5 leaves a remainder of 0).
The last term divisible by 5 less than or equal to 719 is 715 (715 divided by 5 leaves a remainder of 0).
Now, we can calculate the number of terms in the sequence using the formula for the number of terms in an arithmetic series:
n = (last term - first term)/common difference + 1
n = (715 - 85)/5 + 1
n = 631/5 + 1
n = 126 + 1
n = 127
The number of terms in the sequence is 127.
Next, we can calculate the sum of all the terms using the formula for the sum of an arithmetic series:
S = n/2 * (first term + last term)
S = 127/2 * (85 + 715)
S = 127/2 * 800
S = 127 * 400
S = 50,800
The sum of all the integers between 84 and 719 that are divisible by 5 is 50,800.