When Gauss (A German XIXth century mathematician) was at school his teacher asked the class to work out the sum of the first 100 numbers as a way of practising adding whole numbers. To the teacher's surprise, as soon as he had finished setting the exercise Gauss had already found the answer: 5,050.

We are going to use the same process as Gauss did to solve the problem.

If you increase step_1 (1, 2, ...) we can see that pairs of terms equidistant from the centre add up to the same amount.

Try a different number of terms (11, 12, ..., 100, ...) and check that this is still true.

Find the expression which allows us to find the sum of the first n terms. You can find the solution in step_2.

The general formula is given in step_3.

We are going to try and find the sum of the terms indicated in each arithmetic progression below.

12.- Copy the following arithmetic progressions into your exercise book and work out the sum of the terms given:

In each case write down the first term a₁ and the last term a_n, apply the general formula and carry out the operations indicated. The results can be checked in the window.