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(n+3)

Accepted Answer

Hey everyone welcome back in this problem. We have a sequence whose general term is provided and were asked to write the first four terms. And the general term we're given is a. N. Is equal to negative one to the exponent N times N plus seven. So starting with the first term we have a one. So our end value is one. We're gonna have negative one to the exponent one times one plus seven. -1 to the exponent one. This is just gonna be negative one one plus seven is eight. We're gonna get negative eight. We have a value for a one. Now let's move to the second term A. Two. Well this is gonna be negative one to the exponent too Times 2-plus 7 -1 to the exponent to this is just gonna be positive one times nine. We're gonna get a two is equal to positive nine. So we found the first two terms. We have two left find the third term A. Three and is three. And so we get negative one to the exponent three Times 3-plus 7 A negative one to the exponent three. That's an odd exponents. And so we're going to get negative one times 10. I get a three is equal to negative in the fourth and final term that we need to find a four Ns four. So we get negative one to the exponent four times four plus seven a negative to an even exponent. This is going to give us a positive so positive one times 11. And so we get an A four value of 11. Okay. And so the first four terms of our sequence are negative. 89 negative 10 11. This is going to correspond with answer B. 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(n+3)

Key Concepts

Sequences

General Term

Evaluating Expressions

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