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What is the value of the arithmetic series 28+30+32+...+86?

 Jan 4, 2020
 #1
avatar+31 
+2

You can evaluate it as the difference of two sums (relating problems to similar problems).

One sum is 0+2+4+6+8+...+86.

 Jan 4, 2020
 #2
avatar+1076 
-1

Solution: 1,710

 

Divide the series by two; we can multiply by 2 later.

14+15+16+...+42+43.

The formula of finding the sum of the first \(n\) positive integers is \(\frac{n \times (n+1)}{2}\).

We can first find the sum until 43, then subtract the sum until 13 to get the value of 14+15+16+...+42+43.

First plugging in 43, we get \(\frac{43 \times (43+1)}{2} = 946\).

Then plugging in 13, we get \(\frac{13 \times (13+1)}{2} = 91\).

\(946-91=855\).

We still need to multiply by 2 to get our final answer. 

\(855 \times 2 = 1710\).

 

You are very welcome!

:P

 Jan 5, 2020
 #3
avatar+276 
+8

thanks!

 Jan 5, 2020

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