The sum of the first n counting numbers 1 + 2 + 3 + 4 + 5 ... + n is given by S = n/2(1 + n).
a) Find the sum of the numbers 14 to 40 inclusive
Answer is 729. But i don't get why.
Someone explain what the qestion means by "inclusive" please ><!
you want the sum of the numbers from 14 to 40 inclusive (the inclusive means that the number 40 is to be included in the count)
the formula you have given only works if we start at 1
so why not find the sum from 1 to 40, then the sum from 1 to 13 and subtract that.
Wouldn't you end up with only those from 14 to 40 added up??
Let me know what you got this time.
When a question states that a range is "inclusive," it means that both the starting and ending numbers are included in the sum. In the case of the given question, it states to find the sum of the numbers from 14 to 40 inclusive, which means you need to include all the numbers from 14 to 40 in your calculation.
To find the sum of a series of consecutive numbers, we can use the formula S = n/2(1 + n), where S represents the sum and n represents the last number in the series.
In this case, the last number in the series is 40, so we can substitute n = 40 into the formula:
S = 40/2(1 + 40)
= 20(1 + 40)
= 20(41)
= 820
However, this is the sum of all the numbers from 1 to 40 inclusive, not just from 14 to 40 inclusive. To find the sum only for the range 14 to 40 inclusive, we need to subtract the sum of the numbers from 1 to 13.
Using the same formula, we find the sum of the numbers from 1 to 13:
S = 13/2(1 + 13)
= 13/2(14)
= 13(7)
= 91
Now, to find the sum of the numbers from 14 to 40 inclusive, we subtract the sum of the numbers from 1 to 13 from the sum of the numbers from 1 to 40:
820 - 91 = 729
Therefore, the sum of the numbers from 14 to 40 inclusive is 729.