recursive formula for geometric sequence

#Recursive formula for geometric sequence how to
#Recursive formula for geometric sequence plus
#Recursive formula for geometric sequence series

G of N is equal to, and so, let's see, if we're going to, when N equals one, if N is equal to one, With G of N since it's on this table right over here. Recursive function a different, well, I got, I'll stick In a lot of ways, the recursive definition is a little bit more straightįorward, so let's do that. G of N recursively? And I encourage you to pause But this is algebraicallyĮquivalent to this, to our original one. You're starting at 168 and you're multiplying by one half. This one makes a littleīit more intuitive sense, it kinda jumps out at you,

#Recursive formula for geometric sequence plus

So, we could rewrite this whole thing as 168 times two is what? 336? 336, did I do that right? 160 times two would be 320, plus 16, two times eight, so yeah, 336. Well, one half to the negative one is just two, is just two, so, this is times two. The N, times one half to the negative one. Here is the same thing as one half to the N. One, that's the same thing as one half, let me write this. Properties a little bit, we could say G of N isĮqual to, let's see, one half to the N minus Another way you could think about it is, well, let's use our exponent And you can think of it in other ways, you could write thisĪs G of N is equal to, let's see, one way you could write it, as, you could write it as 168,Īnd I'm just algebraically manipulating it over Nice explicit definition for this geometric series. You're gonna multiply by one half twice, and you see that right over there. If N is two, well, two minus one, you're gonna multiplyīy one half one time, which you see right over here, N is three, you're gonna multiply by one half twice. If N is equal to one, you're going to have one minus one, that's just gonna be zero. Like whatever term we're on, we're multiplying by one half, Fourth term, we multiplyīy one half three times. Third term, we multiplyīy one half two times. The second term, we multiplyīy one half one time. Gonna multiply by one half? The first term, we multiplyīy one half zero times. So, we could view the exponentĪs the number of times we multiply by one half. Well, one way to thinkĪbout it is we start at 168, and then we're gonna multiply by one half, we're gonna multiply by one If I say G of N equals, think of a functionĭefinition that describes what we've just seen here starting at 168, and then multiplyingīy one half every time you add a new term.

#Recursive formula for geometric sequence how to

Of N, how can we define this explicitly in terms of N? And I encourage you to pause the video and think about how to do that. Times, it's often called the common ratio, times one half. We're starting at a termĪnd every successive term is the previous term And then to go from 84 to 42, you multiply by one half again. Say we subtract at 84, but another way to think about it is you multiply it by one half. If we think of it as starting at 168, and how do we go from 168 to 84? Well, one way, you could The first term is 168, second term is 84, third term is 42, and fourth term is 21,Īnd we keep going on, and on, and on. Say this is the same thing as the sequence where It is that this function, G, defines a sequence where N The sequence above shows a geometric sequence where we multiply the previous term by $2$ to find the next term.- So, this table here where you're given a bunch of Ns, N equals one, two, three, four, and we get the corresponding G of N. Geometric sequences are sequences where the term of the sequence can be determined by multiplying the previous term with a fixed factor we call the common ratio. So, let’s begin by understanding the definition and conditions of geometric sequences. We’ll also learn how to identify geometric sequences from word problems and apply what we’ve learned to solve and address these problems.

We’ll also learn how to apply the geometric sequence’s formulas for finding the next terms and the sum of the sequence. We’ll learn how to identify geometric sequences in this article.

Geometric sequences are sequences of numbers where two consecutive terms of the sequence will always share a common ratio. We cab observe these in population growth, interest rates, and even in physics! This is why we understand what geometric sequences are.

#Recursive formula for geometric sequence series

Geometric sequences are a series of numbers that share a common ratio. Geometric Sequence – Pattern, Formula, and Explanation