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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
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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

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