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Given the sequence 2, -3, -8, -13 ... determine the formula forthe greatest term (tn). Show your work (INCLUDE THE FORMULA YOU USED, SUB IN THE NUMBERS, THENSIMPLIF...

Question

Given the sequence 2, -3, -8, -13 ... determine the formula forthe greatest term (tn). Show your work (INCLUDE THE FORMULA YOU USED, SUB IN THE NUMBERS, THENSIMPLIFY).

given the sequence 2, -3, -8, -13 ... determine the formula for the greatest term (tn). Show your work (INCLUDE THE FORMULA YOU USED, SUB IN THE NUMBERS, THEN SIMPLIFY).



Answers

Find the indicated term of each geometric sequence. 13 th term of the sequence $\frac{1}{3}, \frac{2}{3}, \frac{4}{3}, \frac{8}{3}, \ldots$

Okay, let me write the sequence. Negative three called comma to come on. Negative. Four comma. 38 Let me just put it in this form. Four out of 38 out of nine. And so on. Okay, so you cannot really see it, but I could have got a hint over here. Negative. Four third and 8/9. Okay, that was a big hint. So it's clear that top number is easy to 48 Um, let's just ignore the first time. 248 Their part two. Okay, so let me write that down. Thes air Power's up to I'm gonna figure that out later, okay? All right. So let's just ignore, Okay, so two minus four in a their powers up to and we also do know it's gonna be alternating right. Minus, plus minus plus and minus. Plus. Right. Okay. So let me write that. Also down Alternating. Okay. And that means alternating minus one to department. Okay, you guys will be including this factor. Okay. Later. Okay. Now, um, this over here, denominator. Here three and nine. Okay. And I didn't really write the last time over here. It was also powers of three So it's times three times. Three times three. But here it's too. And monastery. There are a whole whole number. So what I'm going to do, I'm gonna make a change. So I'm going to make this guy here. Uh, this guy will, um your problem, Because three and nine and this one should be denominator one. So to over one, it's not gonna hurt you. So to over one monastery. However, this one here, let me put put blue this *** three. I can't do this. Negative. Let's go negative outside. And I can put one and one there. I can do that. Because here, 93 and one and one third. Okay, you're keep dividing by three. Okay? And we do know that we do know negative 1/1 3rd is equal to the naked three. Okay, so it works. Okay, So we found everything. All the pieces. Okay, we know we found its alternating. Also, the numerator is always going to be powers up to, and the bottom number is always going to be What powers of three. Okay, So, powers of three, we just confirmed everything. Okay, Good. So all pieces together as a Ben is gonna be equal to, um, since you're starting from minus. So we can just use minus one to the power van, right? So minus one to the power event. Let's just write that down. We can modify later and times, and, uh, the top number is a powers of two. But we started from one, right? So that means to the power of and minus one. Okay. And over this is powers of three. But also, we start from one. Right, so, uh, minus one. Okay, so we were pretty much done. Okay. So you can just put negative one to the power event. Since we're not, we don't have a matching power. So we cannot really combine these two factors, but we can separate them. It's fine. We can, uh, put in a single exponent, though, for these two. So two third raised. The problem minus one will be our answer.

Your eggs or Estefan, the some And so we can't. We can see that there are six numbers in this list. Ace of one is the first number, and that is 3/8 times. One month is the ratio. What are we multiplying by? And we can tell that that's going to be four. So we're gonna do four to the sixth over. One minus four Putting that in her calculator leads us to 511th 0.875

In this question Here we're calling abound. Geometric sequence. Yeah, which on the formula I am equal Do the first term times when the common ratio. Well, I minus one in this question. Here, we've given the sequence three administrator up to 304 Ministry out of eight. Notice that Teoh go to the next term. Here they would try Thio equal to the monastery and the jury divided by three. Then we get equal to the minus a half. So this one good times when the minus a half here and then this one again. And we try to tempt when the minus a half we get the next term here so it doesn't again. We're trying to terms minus a half. We get the next time. Therefore the next time he could be computed by times minus a half, which is equal to the 3/16. And then if you try to multiply with minus a half again to get the next time will be the Ministry over 32. Therefore, the general terms I am equal Jew. The first time will be the three times with the common ratio has B minus one half about an and minus one. This will be the formula. What

Let's find a formula for the general term of this sequence. So we see that we're starting off with three. Then how are we getting to two? Are we getting there by adding, or by multiplying? Well, if we didn't get there by adding would have to add five. But if we add five to two, we'd get to seven. Not negative for over three. So perhaps this is a she measured sequence, and here were multiplying. Bye. Negative. Two over three. So if we start off with three negative three multiplied by negative to over three, you get to two times negative to over three negative for over three, which is over here and so on. So it looks like we take to find a n. You start off with the first term, and then you multiply by negative to over three and minus one times. So this is the formula for the end of term of the sequence, and that's our final answer.


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