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

Question

Philoid · Accepted Answer

Given, a = a

Last term, l = l

We have to prove that the sum of the m^th term from the beginning and m^th term from the end is (a + 1)

Now, m^th term from the beginning,

a_m(b) = a + (m – 1) l

= a + ml – l (i)

Again m^th term from the end

a_m(e) = l – (m – 1)l

= l – ml + l = 2l – ml (ii)

By adding (i) and (ii), we get

a + ml – l + 2l – ml = a + l

Hence, proved

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

If an A.P. consists of n terms with first term a and nth term ls how that the sum of the m^th term from the beginning and the m^th term from the end is (a+l).