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 = n + 5

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we have the sequence A. Is equal to two plus N. And we want to determine if the sequence is arithmetic geometric or none and if it's a medic we want to find the common difference and if it's geometric we want to find the common ratio. So in order to get started with this problem and just looking at the sequence I'm going to go ahead and just look at the terms in the sequence at the different and values. So my first term is one. N is equal to one. And if I plug in one for the value of N I have two plus one or three. If I look at the second term where N is equal to two I have two plus two which is equal to four. If I look at my third term I have two plus three is equal to five. And if I look at my fourth term I have two plus four Which is equal to six. And from here you can see that these terms are increasing by one. So because we're adding a constant to the previous term to get the next term this is an arithmetic sequence and we can find the common difference by subtracting the first term from the second term. So I'm gonna do note the common difference as D and D. Is equal to the second term, four minus the first term three. So the common difference is one. So I solved that it is an arithmetic sequence and the common difference is one. So this becomes my final answer for this problem, and you can see that that aligns with answer choice B. So hopefully this video hoped and see you next time.

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 = n + 5

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