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Evaluate the sum. (Hint: rewrite the fra04n2 Tt 9 n=]...

Question

Evaluate the sum. (Hint: rewrite the fra04n2 Tt 9 n=]

Evaluate the sum. (Hint: rewrite the fra 0 4n2 Tt 9 n=]



Answers

Evaluate each sum using a formula for $S_{n}$. $$\sum_{i=1}^{9}(2 i-14)$$

Fines or partial some using our equation. S seven. In this case, RN value is 12. So this is equal to 12/2 times our first term. That post or 12 terms. So we call that just equation. Here is our arithmetic sequence, so we can find a one m a 12 from that. So it's this quote that in this is a full size and then we want a 12. With wall. You have data four times 12 plus nine, which is equal to negative. 39. Okay, so let's go grab in. So that's 12 worth over to just six and then we have a one that's five minus 39. Let's put that into our jobs better here. So we see there are some is equal to 204

Right, so here we have three times 0 -2 glass, three times one minus two. Uh huh. Period Times two so three times 3 -2 mm. Committee time is for the minister. Okay. And uh this becomes negative too, Plus one. This is six two. That's four. Mhm. 9 -2. That's seven, 12 minus two. That's good. And ah when you add this up, I said, this is too to this plus two, two plus one is three. That's 20.

In this problem of sequence and cities, we have to evaluate the submission that it and its called toe 12 75. Where here? 20. This is 12 and minus nine and now we have to evaluate it. So this can we return it 12 times the mission off And were the lower limited in its called toe 12 75 minus. This will be submission off nine from any school. Two went to 75. So this can wait until 12. And this is just some off first and natural number were any school to 75 So this will be a 75 multiplied with 75 plus one. So this would be 76 divide with two and this over here 75 multiplied with tonight and now we have to evaluate it. So this will be here. Six multiplied with this will be canceled with six. So there were six multiplied with 75 multiplied with 76 minus 75 multiplied with nine. So when we evaluate it, we get six multiplied with 75 multiplied with 76 which is equals toe 342,000. This 4200 minus. This is 75 multiplied with nine, which is equal to 675. And now we have to evaluate it. So that's what we 342 100 minus 600 75 is equal to 33. That will be 33,525. So this is the value off submission 12 and minus nine were, and it's called to one. The lower limited on the upper limit is 75 so this is a result.

So this some, he calls some of K kube came from one to end has two times as some of k squared Came from 1 to hand. My nurses, I'm okay Came from one trillion And then plus four times The summer one came from from 1 to N. According to this formula. This term you calls and squared times and plus one squared or four Last two times. Then according Josie's formula, this echoes and times um 10 plus one Times two. n plus one over six and the miners according to this formula, this you calls 10 times plus one over to communism plus four. And so this echoes And to the 4th past two and Cubed glass and squared over four plus two and kill Past three and squared plus and over three Miners and squared over two. Press fall in and jesse calls screen and the 4th past six and killed last three and squared over 12 of course AIDS and killed us 12 and squared was full and over 12 miners six and squared plus six and or 12 plus 48 and over 12. And as he calls straight into the force plus 14 and cube cross No and squared Plus 46 and over the hills.


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