Write out the first three terms and the last term. Then use th...

Question

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

$\sum_{i = 1}^{100} 4 i$

Accepted Answer

hey everyone in this problem we are asked to identify the first four terms and the last term. And evaluate the some using the formula given which is S. N. Is equal to N. Over two A. One plus A. M. Okay. Alright so let's work over here. The first term. Well this is gonna be we're starting at I equals one. So our first term is just going to be when I is equal to one And the term is going to be six Times I which is gonna be six times 1. I was just gonna be equal to six. Okay. The second term similarly we're starting at I and we're going up by one each time. Okay so the next term is gonna be when I is equal to two in this case we're going to get six times two. That's gonna be 12 mm 3rd term. Same thing. We're going up by one each time. So our eye is going to be three we're gonna get six times three. It's going to be our term right. Six times I i is three we get six times three is 18. The fourth term. Well following the pattern I is equal to 46 times I. Six times four we got 24. Okay. Alright so we've done our first four terms now it wants to know the last term. Okay and when we have a sum like this the last value of I is gonna be this value on the top here. Okay so we're gonna go from I from one all the way to 110. And so the last term Is going to be when I is equal to given by that red circle. Well this is gonna be six times 110 which is going to be equal to 660. Alright. So we found our first four terms. We found our last term. Let's evaluate the some were given the following formula for the sum S. N. Is equal to N over two times a one plus A. M. Now in this case and is the number of terms we're going from 1 to 110. So we have 100 and 10 terms. Okay. It's the upper limit when we're starting at one, it's just going to be the upper limit On I. Okay, so in this case we're gonna have 110 divided by two Times A one while a one is our first term We found that that's six. Okay. And A N. Is the term we know that N is 100 and 10. So A N. Is the 110th term or in other words the last term which we found to be 660. So now we have the sum is equal to 110 over two times six plus 6 60 Which is equal to Times 666. Okay, this is going to be 36,000. 630. Okay. And so if we're looking for the answer, we have our first four terms 6 12, 18, 24 we have a last term of 6 60 with a sum of 36,630 we're going to have answer B. That's it for this one. Thanks everyone for watching. See you in the next video.

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
$\sum_{i = 1}^{100} 4 i$

Key Concepts

Arithmetic Sequence

General Term of an Arithmetic Sequence

Sum of the First n Terms of an Arithmetic Sequence

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