In Exercises 1–12, write the first four terms of each sequence wh...

Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n+1/(2^n−1)

Accepted Answer

Hey, everyone in this problem, we're giving a sequence whose general term is provided. And we're asked to write the first four terms. And the general term we're given is A N is equal to negative one to the N plus one divided by three to the N minus one. OK. All right. So the first term is gonna be a one, this is gonna be negative one to the exponent one plus one. KN is one in this case divided by three to the end which is three to the one minus one. And this is gonna equal to one half. OK? Negative one to the exponent two, negative one times negative one. We get a positive one. All right. Now let's do A two, A two is going to be negative one to the exponent two plus one divided by three to the exponent N which is two minus one. This is gonna give us, we have negative one to an A exponent I have three. So this is gonna give us negative one divided by nine minus one. So we're gonna get negative 1/8. All right. So we found a one, we found a two now let's move on to a three. OK? A three in this case is negative one to the exponent N plus one. So three plus one divided by three to the exponent N which is three minus one. This is going to be equal to negative one to the exponent four. OK? We have a negative to a even power. We're gonna get a positive. So we have positive one divided by 27 minus one which is gonna give us an A three of 1/26. In our final term that we're looking for a four. The fourth term maybe we get negative one to the N plus one which is four plus one divided by three to the exponent N so three to the exponent four minus one. Yeah, we have minus one to the exponent five which is an odd number. So we're gonna get negative one divided by 81 minus one and this gives us an A four value of negative one over 80. So the solution we have the first term is a half, the second term is negative 1/8. The third term is 1/26 and the fourth term is negative 1/80. So we have c thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n+1/(2^n−1)

Key Concepts

Sequences

General Term of a Sequence

Evaluating Expressions

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