The sum of the first n terms of an arithmetic progression is 4n² - n.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The sum of the first terms of an arithmetic progression is . Find the first term, the common difference and the th term.
Need a reminder? The key ideaShow
To find how many terms give a sum, put the sum into and solve the quadratic equation in ; keep the natural-number roots. To find or , put in the known values and solve. From a formula for , the th term is , and .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The first term. .
Step 2. The general term. .
Step 3. The difference. , so .
Step 4. The 10th term. .
Answer: first term , common difference , and th term .
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