Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive mul...

Question

Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive multiples of 3.

Accepted Answer

Welcome back. I'm so glad you're here. We've got an arithmetic series here, six plus 12 plus 18 and so on. All the way up to 570. And we look at those and we see that those are all positive multiples of six including 570. That is 95 times six. And we are looking for the total value of the sum of the 1st 95 positive multiples of six. So all of those numbers added together. That's a lot thankfully. We've got a formula for that. We recall from previous lessons that the summation formula For the numbers all the way up to the 10th term, RN divided by two times A sub one, the first term plus a sub n The 10th term that we're looking for the value of it. So now we can fill in for end because we know that we're looking for the 95th term and all of the sum the sum of all of the numbers proceeding it. So we've got 95/2 times a sub one plus a sub 95. And now let's figure out the values of a sub one and a sub 95. 1st and 95th terms a sub one. The first term is six A some 95. We already looked at that, that is 570 and now we can bring the rest down. So we've got 95 divided by two times six plus 570 doing the parentheses for six plus is 576 times 95 divided by two. A calculator tells us that that is 27,000, 360. We look at our answer choices and that is answer choice C Well done, we'll catch you on the next one.

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Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive multiples of 3.