Find the sum of all 11 terms of an A. P whose middle most term is 30?

1.	Find the sum of all 11 terms of an A. P whose middle most term is 30?
Answer» Let a be the first term and d be the common difference of the given A.P.Clearly, in\xa0an A.P. consisting of 11 terms,\xa0{tex} \\left( \\frac { 11 + 1 } { 2 } \\right) ^ { t h }{/tex}\xa0i.e. 6th term is the middle term.{tex}\\text{ it is given that the middle term =30}{/tex} So a+5d=30 .....(1).{tex}S_{11}=\\frac{11}{2}(2a+10d){/tex}= 11(a+5d) But a+5d=30 from (1)Hence S\u200b\u200b\u200b\u200b\u200b\u200b11\xa0= 11 × 30= 330

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