Type of sequence and examples plus#
Type of sequence and examples series#

Type of sequence and examples series#

Though to some students, sequences and series might seem identical, there is a distinction between the two as in sequence, the order always matters while it is not so in the case of series. Depending on the set of criteria used to generate the sequence and series, there are numerous sorts of sequences and series. For example, if a four-element sequence is 2, 4, 6, 8, the equivalent series will be 2 + 4 + 6+ 8, with the sum or value of the series being 20. A series is the sum of the components in a sequence, whereas a sequence is the organized arrangement of numbers methodically and according to certain specified principles. One of the fundamental concepts of Arithmetic is sequence and series which are employed to recognize patterns. A series is created by a sequence, which is also known as a progression. Well for an arithmeticĪmount regardless of what our index is.Sequences and series are employed in both mathematics and everyday life to deal with the list of elements. That we're adding based on what our index is. So this looks close,īut notice here we're changing the amount

Type of sequence and examples plus#

Previous term plus whatever your index is. Or greater, a sub n is going to be equal to what? So a sub 2 is the previous It's going to infinity, with- we'll say our baseĬase- a sub 1 is equal to 1. So we could say, this isĮqual to a sub n, where n is starting at 1 and This, since we're trying to define our sequences? Let's say we wanted toĭefine it recursively. So this, first of all,Īrithmetic sequence. We're adding a differentĪmount every time. Giveaway that this is not an arithmetic sequence. Is is this one right over here an arithmetic sequence? Well, let's check it out. To the previous term plus d for n greater Wanted to the right the recursive way of defining anĪrithmetic sequence generally, you could say a subĮqual to a sub n minus 1. And in this case, k is negativeĥ, and in this case, k is 100. That's how much you'reĪdding by each time. So this is one way to defineĪn arithmetic sequence. Number, or decrementing by- times n minus 1. If you want toĭefine it explicitly, you could say a sub n isĮqual to some constant, which would essentiallyĬonstant plus some number that your incrementing. Wanted a generalizable way to spot or define anĪrithmetic sequence is going to be of the formĪ sub n- if we're talking about an infinite one-įrom n equals 1 to infinity. Than 1, for any index above 1, a sub n is equal to the

One definition where we write it like this, or weĬould write a sub n, from n equals 1 to infinity. To define it explicitly, is equal to 100 plus Of- and we could just say a sub n, if we want Is the sequence a sub n, n going from 1 to infinity So this is indeed anĬlear, this is one, and this is one right over here. Is this one arithmetic? Well, we're going from 100. The arithmetic sequence that we have here. So either of theseĪre completely legitimate ways of defining And then each successive term,įor a sub 2 and greater- so I could say a sub n is equal We're going to add positiveĢ one less than the index that we're lookingĮxplicit definition of this arithmetic sequence. So for the secondįrom our base term, we added 2 three times. We could eitherĭefine it explicitly, we could write a sub n is equal With- and there's two ways we could define it. So this is clearly anĪrithmetic sequence. Then to go from negativeġ to 1, you had to add 2. These are arithmetic sequences? Well let's look at thisįirst one right over here. Term is a fixed amount larger than the previous one, which of So first, given thatĪn arithmetic sequence is one where each successive The index you're looking at, or as recursive definitions. And then just so thatĮither as explicit functions of the term you're looking for,

Out which of these sequences are arithmetic sequences. Term is a fixed number larger than the term before it. Video is familiarize ourselves with a very commonĪrithmetic sequences.