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# help

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93
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What is the sum of the series 7 + 10 + 17 + 24 + ... + 479?

May 3, 2020

#1
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7 + sum_(n=1)^68(7 n + 3) = 16,633

May 3, 2020
#2
+732
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Hi guest!

The formula for a series is $$\frac{a_1+a_n}{2}\cdot n$$

n = how many terms there are

So, we know $$a_1=10$$ since it's the first term (in this case let's save the 7 for the end, since it doesn't follow the pattern)

$$a_n=479$$ since it's the last term

There are 68 terms because there are 479-10=469, 469/7 = 67 terms, but you have to add 1 since we didn't count 10, so there are 68 terms.

Now, all we have to do is plug the equation in!

$$\frac{10+479}{2} \cdot 68=16626$$. We have to add that first 7 too, so $$16626+7=\boxed{16633}$$.

I hope this helped you, guest!

:)

May 3, 2020