How many terms of the $\mathrm{AP}: 9,17,25, \ldots$ must be taken to give a sum of $636 ?$

Answer

Related Courses

Precalculus

NCERT Class 10 - Math

Chapter 5

Arithmetic Progressions

Section 3

nth Term of an AP

Discussion

You must be signed in to discuss.

Top Precalculus Educators

Watch More Solved Questions in Chapter 5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Video Transcript

We are going to do problem # four discussion. We have to find The number of terms. Okay, up to which if we add that ap if we had that sequence we will get some of that terms is 636. Let's say We are a little and terms. So some of anthem is given that is 636. So we need to find the value of an From the given sequence that sequences 9, 17, and so on. Where a in this case is nine. First time and difference in this case is 17 minutes nine. That is eight. Okay. Now we have it. We have now common different set eight and we have a that is nine and we know that some of aunt um this is written as and by two multiplied to to a plus And -1 multiplied to be. So it was just put this value and find the relevant some of it. In terms of 636 equals to end by two Multiply to 29. That is 18. Okay. Plus and -1 multiplied to it. Now This is 636. And divide this to the inner part of this. This one that is in brackets. So we're getting n equals two and multiply to not equals and multiply to get invited. That is nine plus And -1 multiplied to 4th. Okay now you're just solving this further. So we are getting this is 636 this is equals, This is nine n nine and and this is multiplied to four and and this is multiplied to end minus. Well Okay so we're getting this is 636. This is equals to nine and Plus four and square minus foreign. So from here we're getting this has 636 equals two for an esquire nine in -4. In the days The last five and no we are getting here this is zero equals to four. Any square plus five and -636. Okay So we need to find development by solving this crowded evacuation. So for that we need to just uh you can just do it like this only by writing it as the farmer quadratic solution for that equation. And so this is any calls to minus beast would be in this case is five. So this is minus five plus minutes. And the root of B squared B squared in this case is 5 25 -4- four. That is foreign to aim to see as many as 636. This is divided by two into 4. That is it. We are just they donate as But the quadratic solution we write for X. That is the cause tremendous B plus minus and the root of The Scar -4 a. c. by the way. Okay. This is what we do here. We'll just see how much where you're just coming out there. That n equals 2 -5 plus minus Under router. This is 25 And 14- four. That is 16. 16 multiply 2- 16. Multiplied to 636. This is giving us 10176 with a positive sign. 1017 six. So this is divided by eight. Okay From here we're getting n equals two and equals true. Man is five plus. Menace on the road off 10176-plus 25. So this is equal to 110201 divided by eight. Now let us find the Squire out of this town. That is Square root of 10201. So this is a constant 101. This is -5 plus minus 101 divided by eight. Okay So we got two values of and from there that n equals two -5 -101 x eight. Another one is Menace five Man Plus 101 x eight. Okay. As we can't take this negative value. Okay, this is negative value. So a number of times cannot be a negative value. So we will not consider this. Well consider this positive one. So this will be equals two unless 96 divided by eight. So this is nothing but eight ones are eight and eight to Eur 16. So this is any construct 12. So we got if we Add sequence to 12 term then we'll be getting The some S 636. So this is the answer. That's all. Thank you.

We have video lessons for 98.48% of the questions in this textbook