Nemo scoring last submission is used for your score Kuntioenol submis:8S points Previous Answers #swokPreCaic12 9.1.001 Find the first four terms ad the eighth term...

The first 3 terms and the last term of an arithmetic sequence are given. Find the number of terms. $$3 \frac{1}{8}, 4 \frac{1}{4}, 5 \frac{3}{8}, \ldots, 14 \frac{3}{8}$$

This problem, we want to find the first four terms Yes. As well as a determined sequence generated by three in -2 over n squared plus one. Now, in order to find these terms, it's important to remember that all we're doing here is looking for the values whenever it is 1234 and then again at eight since one of the eighth term. And all this comes down to is plugging in those numbers here in this function. So no those ones three times 1 -2 over one squared plus one. Let's give this 1/2. And so our first term is 1/2 When it is two, this is three times 2 -2 over two squared plus one. And so it's fork fits When it is three, This is three times 3 -2 over three squared plus one. This goes to 7/10 for 1/4 term, This is three times 4 -2 over four squared plus one. Just 10/17. And then we also want the 8th tournament. So when it is eight, yeah, three times 8 -2 over eight squared plus one. We're just 22 Over 65. And so there are the first four terms As well as the 8th time. Yeah.

So fine in the 1st 5 terms of an arithmetic sequence, it gives us that the first term is poor. It also gives us that the sixth term it's gonna be 39. Okay, So to do this particular problem, I'm gonna use my, uh, formula to find the eighth term. I think the ace of sex is gonna equal ace of one, which is poor plus and minus one times are common difference. And we use this to find, but our common differences. So our ace of six is 39. Our first term is for in minus one would just be five and five times D. So if we subtract four from both sides will have 35. It goes five d drive. Us has about five, and we'll find that are common difference is seven. So now we can list are five terms. Our first term is for they're coming differences seven. So we're gonna go up by seven each time. This would be really easy to check, because our next time should be the six term, which should be 39. It's just our way to check this time. Okay, so there's our first fight terms. Thank you very much.

It's just a ride. The 1st 5 terms of a sequence where the first term is given as negative for and the six term is given as negative 39. Okay, we can use our formula for the end of term so we can say a 76 is gonna equal a sub one plus and minus one, which is five times D so he uses to find our common difference. We're gonna have negative. 39 is equal to negative for plus five d. You can add for the both sides get negative. 35 tickle to find d. So dividing both sides. About five. We can see that d is gonna be negative. Seven. Writing our 1st 5 terms. We're gonna start with negative four and we're gonna go down seven each time. So the native 11 negative. 18 Negative. 25. The negative. 32. Really easy way to check to see that the next term is gonna be negative. 39. Which matches our ace of six. It's that checks. Yes. These are the 1st 5 terms of our sequence. Thank you.

For this problem. We were given an equation. Were asked if in the 1st 5 terms, as well as finding our eighth term. But let's find the eighth term first. My term is going to be four plus three times. This is 24 plus four. My answer is 20 looks Go ahead, buy the next one. We know that our first term is going to be or plus three times one four plus three seven for plus three times two is four plus six, 10 or plus three times three is four plus nine celebs 13 for plus three times four well plus four It's Eckstine and the last one for list three times five 15 plus four me night.