Find the sum of the first 18 terms of 40, 37, 34, … Are all 18 terms positive?
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Find the sum of the first terms of Are all terms positive?
Need a reminder? The key ideaShow
The sum of the first terms of an arithmetic progression is , or when the last term is known. The sum of the first natural numbers is .
The worked solution
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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 numbers. , , .
Step 2. The sum. .
Step 3. The last term. . The terms after are negative: .
Answer: ; no, the last four terms are negative.
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