5

QUESTIONEncontrar enesimo temino de las sucesionesan = ] -(n + 1)In=} (n + 193(n + 122QUESTIONEncontrar el enesimo termino de las sucesiones 5,7,9,11, 2n + 3Zn-3Zn+...

Question

QUESTIONEncontrar enesimo temino de las sucesionesan = ] -(n + 1)In=} (n + 193(n + 122QUESTIONEncontrar el enesimo termino de las sucesiones 5,7,9,11, 2n + 3Zn-3Zn+22n = 2QUESTIONEncontrar el enesimo termino de las sucesiones 12,36 , 108, =4,3"+1Dn =4,34.320+14.32n -

QUESTION Encontrar enesimo temino de las sucesiones an = ] - (n + 1) In=} (n + 193 (n + 122 QUESTION Encontrar el enesimo termino de las sucesiones 5,7,9,11, 2n + 3 Zn-3 Zn+2 2n = 2 QUESTION Encontrar el enesimo termino de las sucesiones 12,36 , 108, =4,3"+1 Dn =4,3 4.320+1 4.32n -



Answers

Verify each formula for $n=1,2,3,$ and 4 $$\begin{array}{l} 1(3)+2(4)+3(5)+\dots+n(n+2)= \\ \frac{n}{6}(n+1)(2 n+7) \end{array}$$

First term in our second term over mathematics secrets. So since the two are consecutive terms, we confined our common difference of people to 1/4, minus 1/6. So it's that equal to direct, equal to 1/12. Okay, so using our common difference on our first time, we can drive or end of term over Eric manic secrets that you go to our first term plus and minus one that times are common difference. Now you think this Let's find a 19. That's one of the six plus 19 months. 1/4 times, one with wall. So let's put that into our tracking there. To see what yet. Okay, so this gives us, um 5/3. Now we confined us of 19. That's if we use our taken form. That's 19/2 times the first time. That's 1/6 plus or 19th term, which is found here. So people to 53 So putting this into our Johnson later. Let's see what we yet so whatever six cost five or three. That gives us 17.416 bar

All right, so we have you over three. Q minus nine minus 3/4. Q plus 12 equals seven Q squared plus six. Q plus 63. All over 24 Q squared minus 2, 16. I'm going to factor out A three here and I get q minus three, factor out of four here and I get Q plus three, factor out of 24 here. And I get Q squared minus nine which is Q plus three Hugh minus three. So now when I take my first my LCD will be 24 times Q plus three q minus three. So when I multiply that by Q over three Q minus three, three goes into 24 8 times and the q minus three cross out and I'm left with eight Q times Q minus three. That's right. So the q minus three crosses with the q minus three and I'm left with eight Q times Q plus three. And then I'm gonna take my LCD 24 Q plus three Q minus three times my second fraction which is three over four Q plus three mike. You plus wow, Q plus threes cancel four goes into 24. 6 times six times three is 18 times a quantity Q minus three. And when I multiply the second fraction, I'm sorry the third fraction times the LCD the entire denominator drops out and I'm left with seven Q squared plus six Q plus 63. When I distribute I get eight Q squared plus 24 Q minus 18 Q plus 50 four. I distributed that equals seven Q square. Well six Q plus 63. So we're dealing with quadratic, we want to move everything to one side. So I'm going to subtract all of my right side minus seven Q squared minus six Q minus minus 63. So I have one Q squared here, I have 24 q minus 18 which is six. And then I'm attracting six queues. So that gives me zero cues and 50 for minus 63 gives me minus nine equals zero. So when I factor that I get Q plus three Q minus three equals zero, which means Q equals negative three or Q equals three. When I go back up and put that into my denominators, I can't if I put a three here, that's going to give me a zero in my denominator and if I put a negative three in this one that will give me a zero my denominator. So neither of these answers work. So this one is no solution. Mhm.

All right, so we have to prove our n equals one piece. So are left hand side. We just have seven. All right hand side. We're gonna get one times. Three times one plus 11 well divided by two. So we keep gone. Made it seven is equal to one times 14 over to just seven. That is our one case equals two. We have seven. Plus 10 is equal to times three times two plus 11 all divided by two. Now, if we add these together in the left hand side because 17 that's gonna be equal to on the left hand side are to cancel, But we just have three times two plus 11 which is just 17. So that proves R N equals two case and equals three. Next to me of seven was 10 was 13. That's gonna be equal to three. James three times three plus one. Excuse me. 11. Divided by two. It's on the left hand side. Seven plus 10 plus 13. It's just gonna be 30. On the right hand side. We're gonna have three times 20 divided by two, and then we do the math. You just see the pretty is again equal 30. And that proves r N equals three case. Yeah, Lastly, we get an equal support, so we have left hand side seven close to 10. I was 13. I was 16 is equal four times, three times four plus 11 all divided by two under the left hand side. We get 46 on the right hand side. We can cancel out our denominator with, therefore and get two times the quantity of three times for plus 11 which three times for 12 plus 11 is 23. So two times 23 it's just gonna be 46. And that proofs are n equals 123 and four.

We've been provided to equations and we have 200 solution for that question. So the first question is given to us at 1 73 X plus 1 97 Y is equal to 149. And the second equation is given to us as 1 97 X plus 173 Y is equal to 221. We are supposed to find out the value of X and Y point exactly this solution set for them, giving two equations over here. So now let's say this is a question one, and this is equation too. So from equation one, we can get the value of X. So from equation one, X will be equal to 149 minus 197 Y upon 173. Similarly, from equation two, X is equal to 221 minus 173 Y upon 197. Let's say this is a question three. And this is equation for Now, you can easily equate equation three and equation for, isn't it? So that means 149 minus 197 Y upon 173 is equal to 221 minus one and 73 Y upon 197. Now you can just cross market Flower hill. So I'm doing that, we'll get 29,353. My ministry 38809 Why is equal to 38,233 -292. Right, so now, yeah, this is equal to one. Now we're here, you can just combine like terms together. So I'm combining of the like terms together, we'll get minus 38,809 plus 29,929 Y. Is equal to 38,233 minus 29,353. I've just bought the variables on one side and the concerns on the other. So that would be equal to minus 8880 Y is equal to 8880. Like that means why is equal to minus one now that you've got the value of five? Just plug why equal to minus one in? Let's say I'm plugging it over here in equation three right? This is a question three. So I just love it over here in equation three. So I'm doing that, we'll get X is equal to 149 minus 197 times minus one upon 173. So that will be equal to 149 plus 197 upon 1 73. So X will be equal to that means from here to get the value of X. As see this was we have to find out the solution said, that means X is equal to two over here and I was equal to minus one. So, so this is the required answer. So if you just matter from the given options that needs option for is built, correct choice over here.


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