In Exercises 19–21, write a formula for the general term (the nth...

Question

In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. -7, -3, 1, 5 ...

Accepted Answer

Welcome back. I'm so glad you're here. We've got an arithmetic sequence negative four negative 125. So on. And we want to write a formula four and find the value of the 15th term of this aromatic arithmetic sequence. So we know from previous lessons that a sub N. Meaning the value of N term. Any term that we're looking for in our arithmetic sequence is the value of the first term. A sub one plus N. That number term minus one times D. And the end value here that we're looking for. We're looking for the 15th term. So we've got a sub 15 Equals the value of a sub one plus parentheses 15 minus one times D. We can simplify that a little bit 15 minus one. Well that's 14 D. Bring down the a sub one. And we know looking at our arithmetic sequence that the value of the first term, a sub one is negative four. So that will be negative for plus 14 D. Is the formula for the value of our 15th term. And now we just want to solve. Well to solve we need to know what D. Is and we recall from previous lessons the D. Is going to be the difference between two sequential terms. So we can start with a sub two minus a sub one And we'll use a sub two. That's negative one and minus Again Our Friend, -4. So negative one minus a negative four equals positive three. The difference here is three. So we plug this into our calculator negative four plus 14 times three Gives us a value of 38. So a sub 15 equals 38. We look at our answer choices and that matches with answer choice. A while gone will catch on the next one.

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