Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

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Precalculus

NCERT Class 10 - Math

Chapter 5

Arithmetic Progressions

Section 3

nth Term of an AP

Discussion

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Video Transcript

mhm We are going to do problem number eight. And discussion has given that second term is 14 And the third term is 18. We need to find We need to find some of the 1st 50 first time. Okay, So as two consecutive term is given over there that if second time is given and third time is given, so we can easily find common difference. That is the difference between two consecutive terms. So that will be a three men, I say two. So this is 18 men is 14, so this will give us Government difference will be four. Okay. No, we know the next term of sequences written as a plus And -1 in today as second term is 14 so n equals to two will be there. Now we can just easily find here The value of it as this is an issue. So the switch to -1 multiply. It could be that is for So from here this is 14 equals two. A plus one into four. That is four solutions are subtracted For from both sides will be having a equals to 14 minutes for that is 10. Now we got First term, that is 10. We've got common difference, that is four. We can easily find the summer first 51st term some of first trip the first time. Okay, by this expression that action equals to end by two. Multiplied to to a plus and minus one. Including Now here we need to find this summer first 51st time. So this is N equals to 51. We'll be having had 51 by two, multiplied to into 10 Plus and -1. So this is 51 -1 multiply 24 So from here some are 51 time. This will be a constant 51 x two. This is multiplied to pretend that is 20 plus 15-4, that is 200. So from here, Somehow, time this will be equals to 51 divided by two, multiplied to 222. So from her We're getting 51 Multiplied to 110. If we just divide these two with total 20, so we're getting this is 1110. So you can just easily find this multiplication here, that 51 multiplied to 110. So this will give us 5610. This is equals 25,610 as December 1st 51st drum on this sequence. So this is the answer in this case, That's all. Thank you.

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