The first and the last terms of an A.P. are a and l respectively. Show that the sum of nth term from the beginning and nth term from the end is a + l.

Open in App

Solution

Given first term = a
Last term = l
The nth term from starting
$a_{n} = a + (n - 1) d$ ...... (i)
The nth term from end
$= l - (n - 1) d$ ...... (ii)
Adding (i) and (ii), we get
Sum of nth term from beginning and nth term from the end.
= a + (n - 1)d + l - (n - 1)d
= a + l

Suggest Corrections

Similar questions

Q. 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).

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

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

Join BYJU'S Learning Program

The first and the last terms of an A.P. are a and l respectively. Show that the sum of nth term from the beginning and nth term from the end is a + l.

Given first term = a Last term = l The nth term from starting an=a+(n−1)d ...... (i) The nth term from end =l−(n−1)d ...... (ii) Adding (i) and (ii), we get Sum of nth term from beginning and nth term from the end. = a + (n - 1)d + l - (n - 1)d = a + l

Given first term = a
Last term = l
The nth term from starting
$a_{n} = a + (n - 1) d$ ...... (i)
The nth term from end
$= l - (n - 1) d$ ...... (ii)
Adding (i) and (ii), we get
Sum of nth term from beginning and nth term from the end.
= a + (n - 1)d + l - (n - 1)d
= a + l