In Exercises 12–15, write the first six terms of each arithmetic ...

Question

In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2

Accepted Answer

Welcome back. I'm so glad you're here. We are trying to find the first five terms of an arithmetic sequence. So we're trying to find a sub one. The first term a sub to the value of the second term. A sub three. The value of the third term. A sub four. The value of the fourth term and a sub five. The value of the fifth term. What do we know? We already know the first term. A sub one equals four thirds. Yay, fill that one in. What else do we know? We know the common difference. D equals negative one third. And so how do we use that common difference? Well, when we are finding a terms value we take the previous term and add the common difference. So to find the second terms value a sub two we take the previous term a sub ones value which is four thirds and add the common difference. So we add negative one third, four thirds plus negative one third gives us three thirds. That is a sub two. Now to find a sub three we take the previous terms value. So that's three thirds from a sub two and we're going to add the common difference. So add negative one third, three thirds plus negative one third gives us two thirds. Great. That's a sub three. To find a sub four. The fourth terms value. We take the previous terms value which is two thirds and we're going to add the common difference two thirds plus negative one third gives us one third, Great to find the fifth terms value. We take the fourth terms value which was 1/3 and add the common difference which is negative one third. So one third minus one third gives us zero. Great Before I bring those all down. Want to point out That 3/ equals one. So written. All together we've got 4/3 one, 2/3, 1 3rd and zero. We look at our answer choices and that matches with answer choice. D. Well done. We'll catch on the next one.

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