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Find the sum of the first 18 terms of 40, 37, 34, … Are all 18 terms positive?

Try 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 $18$ terms of $40, 37, 34, \ldots$ Are all $18$ terms positive?

Need a reminder? The key ideaShow

The sum of the first $n$ terms of an arithmetic progression is $S_n = \dfrac{n}{2}[2a + (n - 1)d]$ , or $S_n = \dfrac{n}{2}(a + l)$ when the last term $l$ is known. The sum of the first $n$ natural numbers is $\dfrac{n(n + 1)}{2}$ .

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.

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