Find each indicated sum.

Question

\sum_{i = 1}^{6} 5 i

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to perform the summation From I equals one 28 for the expression three. I So in this case we want to find the values of the terms from I equals one Through high equals eight For the expression three I so if I start with the first term where I is equal to one, my expression is three times one which is just three. I look at my second term I is equal to two where I is equal to two. My expression becomes three times two. I simplify it six. When I is equal to three my expression becomes three times three I simplify it. I get nine When I was equal to four I got three times 4 and three times 4 is 12 When I have I is equal to five My expression becomes three times 5 and that becomes 15. So you can see I'm really only adding three between terms so I can go ahead and finish evaluating by plugging in the values of I or I can simply add three to my previous answer. I'm just going to finish writing out the plugging in. So I have three times six which is 18. I'm gonna move it down here. So when I equals seven my expression is three times seven simplified. I get 21 And finally when I is equal to eight I have three times eight Which is and from here you can see that I've determined the value for the terms I equals one through I equals eight. But I still need to do my summation so I want to make sure to add each of these values. So I need to add three plus six plus nine plus 12 plus plus 18 plus 21 plus 24. So if I do that Have 3-plus 6 plus nine plus 12 plus plus 18 plus 21 plus I'll start simplifying this. So three plus six is nine, nine plus 12 is 15 plus 18 is and 21 plus 24 is 45. And I can Simplify this again. Where nine plus 21 is 30 and 33 plus 44 is 78. So from here, 30 plus 78 is 108. So this becomes my final answer for the summation for all the terms where I equals one through I equals eight and you can see that 108 aligns with answer choice A So hopefully this video hoped and see you next time

Find each indicated sum. $\sum_{i = 1}^{6} 5 i$

Key Concepts

Summation Notation (Sigma Notation)

Arithmetic Series

Formula for the Sum of an Arithmetic Series

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