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.
#ARITHMETIC SEQUENCE PLUS#
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.
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