Our Discord hit 10K members! 🎉 Meet students and ask top educators your questions.Join Here!

Like

Numerade Educator

Like

Report

General Sequences And Series - Example 1

A sequence is a collection of objects in which repetitions are allowed. For example, the sequence (2, 4, 6, 8, 10) of even numbers can be written as {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, or any other of an infinite number of ways. The numbers in the sequence are called the terms of the sequence. The first number in the sequence is called the first term, the second number is called the second term, and so on. The nth term of a sequence is the number that is the nth member of the sequence. The kth term of a sequence is the number that is the kth member of the sequence.

Topics

No Related Subtopics

Discussion

You must be signed in to discuss.
Top Educators
GH
Grace H.

Numerade Educator

Anna Marie V.

Campbell University

MC
Megan C.

Piedmont College

Kristen K.

University of Michigan - Ann Arbor

Recommended Videos

Recommended Quiz

Precalculus

Create your own quiz or take a quiz that has been automatically generated based on what you have been learning. Expose yourself to new questions and test your abilities with different levels of difficulty.

Recommended Books

Video Transcript

Okay, so this is gonna be the first example out of our general sequences and Siri's, Siri's. And the question says, find the next five terms in Siris. Remember with the secrets. And since series in general, it's all about recognizing the patterns, so you can basically just it's just a lot of times that basically just trial and error. So you kind of think about what patterns you notice and see if that would work or not. And then if it does, I'm great. And if it doesn't, you just move on to the next and just keep trying. So from here, I could see I have 136 and 10. It doesn't really look like it's increasing by any common factor, but what I see is that from here to here, it increases by two. From here to here, it increases by three, and from here to here increases by four, which means that the next next increase test increased by five and then by six, and then by seven. So basically what's going on is we're adding one more then what we added last time. So if we do 10 plus five, that would be 15 So then, if we added fact to get there, so then now we have to add six. It's 21 and since we added six previously, we had. We have to add one more than that, which is seven. So now we have 28 and then now we have to add eight, which is going to give us 36 on then. Now we have to add nine, and that's going to give us 45. So these would be the next five terms in the Siri's again. There isn't, like, always gonna be like in equation for it, and in this case there is. But like, the key point is that you have to think about what kinds of patterns are there and just see what you could do. Just try a bunch of different things until it works.

Johns Hopkins University
Precalculus

Topics

No Related Subtopics

Top Precalculus Educators
GH
Grace H.

Numerade Educator

Anna Marie V.

Campbell University

MC
Megan C.

Piedmont College

Kristen K.

University of Michigan - Ann Arbor