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

Question

Philoid · Accepted Answer

To prove: sum of the n^th term from the beginning and the nth term from the end is a + l

We know, a_n = a + (n – 1)d where a is first term or a₁ and d is the common difference, and n is any natural number, and n^th term from the end is a_n^’ = l – (n – 1)d

Now,

a_n + a_n^’ = a + (n – 1)d + l – (n – 1)d

⇒ a_n + a_n^’ = a + nd – d + l – nd + d

⇒ a_n + a_n^’ = a + l

Hence Proved

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

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