Q. 413.7( 6 Votes )

The first and last terms of an AP are a and 1 respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a + 1).

Answer :

Let d be the common difference of the AP.

First term = a


Last term = l = 1


nth term from beginning of an AP is given by:


an = a + (n - 1)d …………………………….(1)


nth term from the end of an AP is given by:


Tn = l - (n - 1)d


= 1 - (n - 1)d …………………………….(2)


Sum of the nth term from the beginning and end is given by:


an + Tn = a + (n - 1)d + 1 - (n - 1)d


= a + 1


Hence, proved.


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