Find the sum of the first 22 terms of the arithmetic sequence: 5,...

Question

Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, ...

Accepted Answer

Welcome back. I'm so glad you're here. We've got an arithmetic sequence, one negative two negative five, negative eight, negative 11 and so on. We want to find the sum of the 1st 38 terms of that. That is a lot thankfully. We've got great formulas to help us out. We've got the summation notation formula here where we know that the sum of all numbers up to an end term equals that number N, divided by two times a sub one. That's the value of the first term plus a sub N. The value of that final term we're looking for. So in this case that final term is the 38th term. So we've got s of 38 equals 38 divided by two times a sub one plus a sub 38. Let's see what we know A sub one. That's the first terms value that's one And a sub 38. Well we're not given that one in this case so we get to use another handy formula. We recall from previous lessons that a sub any term N equals a sub one. The value of the first term plus and minus one times D. So okay we know that a sub one again is one plus 38 minus one times D. Or in other words one plus 37 times D. But what's D. Well we've got another formula to pull out from previous lessons. We know that D. Is going to be the difference between any two sequential terms and in this case I'll just pick a sub two minus a sub one. There's our friend a sub one again which was one in a sub two. We look up here and that second term is negative two. So negative two minus one that equals negative three. And that makes sense. Going from 12 negative two. We're going down three from negative 22 negative five. We're going down three so D equals negative three. Take that negative three times 20 or plus the one. So 37 times negative three is going to give us negative 111. So one minus 111. The 38th terms value is negative 110. So we can fill that in up here and bring the rest down 38/2 times one minus 110 which is negative 109 inside the parentheses. Times that. 38/2 in front. And we can plug that into a calculator and that gives us an answer of negative 2071. We look at our answer choices and that is answer choice B. Well done, we'll catch you on the next one

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