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If an A. P.  consists of n terms with first term a and n ^th term l show that the sum of the m^th term from the beginning and the m^th term from the end is (a+l).
Asked by rishijuneja2018 | 23 Aug, 2018, 07:31: PM
First term of A.P is a
nth term =l
Let d be the common difference
nth term=a+(n-1)d
l=a+(n-1)d
d=l-a/(n-1) ------------1
Mth term from the beginning =a+(m-1)d
=a+(m-1)(l-a/(n-1) ) ----------------2
Mth term from the end we get:
=l+(m-1)(-d) ......where we consider first term as l and the common difference=-d
=l+(m-1)x(-(l-a)/(n-1))
=l-(m-1)(l-a)/(n-1) --------------3
thus sum of mth term from beginning and end is
=a+(m-1)(l-a/(n-1)) +l-(m-1)(l-a)/(n-1)
=a+l
Answered by Arun | 24 Aug, 2018, 10:34: AM

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