The sum of 1st 7 terms of an AP is 63 and sum of it\'s next 7 terms is 161.Find 28th term of an AP.

The sum of 1st 7 terms of an AP is 63 and sum of it\'s next 7 terms is

1.	The sum of 1st 7 terms of an AP is 63 and sum of it\'s next 7 terms is 161.Find 28th term of an AP.
Answer» Let \'a\' be the first term and d be the common difference of the given AP. Then, using Sn= {tex}\\frac{n}{2}{/tex}{tex}\\cdot{/tex}[2a+(n-1)d], we get,\xa0S{tex}_7{/tex} = {tex}\\frac{7}{2}{/tex}(2a + 6d)Since sum of the first 7 terms of AP is 63 . Therefore,S{tex}_7{/tex}=63{tex}\\Rightarrow{/tex}7(a+3d)=63 {tex}{/tex}{tex}\\Rightarrow{/tex}a+3d=9.... (i)Since sum of the first 7 terms of an AP is 63 and the sum of its next 7 terms is 161.\xa0Therefore, the sum of first 14 terms = 63 +161 = 224.{tex}\\therefore{/tex}S14=224 {tex}\\Rightarrow{/tex}{tex}\\frac{{14}}{2}{/tex}(2a+13d)=224{tex}\\Rightarrow{/tex}7(2a+13d)=224{tex}\\Rightarrow{/tex}2a+13d=32....(ii)Multiplying (i) by 2 and subtracting the result from (ii), we get 7d = 14 {tex}\\Rightarrow{/tex}\xa0d = 2.Putting d = 2 in (i), we get a=9-6=3.Thus, a=3 and d=2.{tex}\\Rightarrow{/tex}28th term of this AP is given byT{tex}_{28}{/tex}=(a+27d)=(3+27{tex}\\times{/tex}2)=57.Hence, the 28th term of the given AP is 57.