what is the sum of the integers from 19 to 45

Question

What is the sum of the integers from 19 to 45 and how do you find it on a Ti-84 Graphing calculator if possible?

Answer 1

The quick answer is you multiply the average of the integers by the number of integers. The average of all the integers will be the same as the average of the first and last. There are (45 - 19 + 1) integers (think of {3,4,5,6} having 6-3+1 integers). It would be tempting to think there are only (45-19) integers, but that would be an OBO error ("off by one error").

So, (19+45)/2 * (45 - 19 + 1) = 864

 

Now, if you wanted a brute force method on a Ti-84, we can do that too.

sum(seq(X,X,19,45,1))

 

You can find the functions in your LIST menu under MATH and OPS.

 

The first argument of seq is the function used, the second is the input of the function, the third is the lowest value of the input, the fourth is the highest value of the input, and the fifth is the increment.