Write the following arithmetic series in summation notation. 8+10+12+⋯+34

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Nathanael Webber · Accepted Answer

Well, let&#039;s see. This sum&#039;s terms increase by 2 each for each subsequent term, so our summand should be something like 2k where k is the summing index. If we just had 2k, with limits of say 11 to 1010, we&#039;d get 10 ∑2k=2(1)+2(2)+2(3)+⋯+2(10)=2+4+6+⋯+20 k=1 OK. That gets us the going up by two part, but not the fact that it should start at 8. It starts at 2 so what we really need is to add 6 to every term. That should shift up the starting point while keeping the spacing between numbers. 10∑[2k+6]=[2(1)+6]+[2(2)+6]+[2(3)+6]+⋯+[2(10)+6]k=1​=8+10+12+⋯+26 Now the only thing left is make sure that the sum stops in the right place. It looks like we are 8 shy. So because we&#039;re skipping every other number, that should mean we need 4 more terms. So let&#039;s try stopping at the indexk=14k=14. 14∑[2k+6]=[2(1)+6]+[2(2)+6]+[2(3)+6]+⋯+[2(14)+6]k=1​=8+10+12+⋯+34 And there we go! We&#039;re all done.

Write the following arithmetic series in summation notation.8+10+12+⋯+34

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