In Exercises 51–56, the general term of a sequence is given. Dete...

Question

In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.

an = 2^n

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we have the sequence A. N. Is equal to seven to the end power. And we want to determine if the sequences arithmetic or geometric or none of them. And if it's arithmetic determine the common difference. If it's geometric determine the common ratio. So in order to get started I'm just going to write out a couple of its terms. So when N is equal to one we have the first term. So if I plug in one into the value of NI get seven to the first power which is just seven. If I look at the second term where N is equal to two, I have seven squared or 49. If I continue with the third term I have seven to the third which is equal to 49 times seven Or 343. You can see that there's a pattern already with our terms Where we're adding seven Or multiplying 7 to the previous term to get the next term. So this is giving me geometric pattern because we have a common ratio. And we can solve for the common ratio. Even though we can already suspect that it's seven. We can sulfur it by Dividing the second term 49 By the first term seven. And that gives us that the common ratio is seven. And we can see that that's true because if we multiply the second term 49 Times seven We get the third term. So now we know that the sequence is geometric and it has a common ratio of seven. So this becomes the final answer for this problem and that aligns with answer choice A oh, not a answer choice C. So hopefully this video helped and see you next time.

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In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. an = 2^n