If an A.P. consists of n terms with first term a and nth term ls how t

1.	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).
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).

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