Question
Wed January 11, 2012 By:

If an A.P consists of n terms with first term 'a' and the nth term 'L' show that the sum of mth term from the begining and the mth term from the end is (a+L).

Expert Reply
Thu January 12, 2012
Here, mth term from last = (n-m+1)th term from begining.
Now Sum of mth term from begining and mth term from last
= am + an-m+1
= a + (m - 1)d + a + (n - m + 1 - 1)d
= 2a + (m - 1 +n - m)d
= a + a + (n - 1)d
= a + an
= a + L
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