ARITHMETIC PROGRESSION Analysis

 6. SUM OF n TERMS IN AN ARITHMETIC PROGRESSION 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. 11.- Let's suppose we want to find the sum of the first ten terms: 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.

7. DETERMINING THE SUM OF n TERMS OF AN ARITHMETIC PROGRESSION

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:

 nº Progression a1 an Sn 100 3, 7, 11, 15, ... 250 -12, -9, -6, -3, ... 87 12, 9, 6, 3, ... 25 -6, -2, 2, 6, ... 1000 10, 3, -4, -11, ... 35 120, 152, 184, ...

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

 Juan Madrigal Muga Spanish Ministry of Education. Year 2002