Question

If m times the mth term of an ap= ntimed the nth term. Show that (M+N)th term of ap=0

Answer 1

Let mth term be am and nth term be an

According to the question :

m(am ) = n(an )

Apply Formula : an = a + (n-1) *d [ a - first term , d -Common Difference , n - No of terms ]

m( a + (m-1) *d ) = n( a + (n-1) *d )

{ma + (m2 - m) d }= [na + (n2 - n) d]

{ma + (m2 d- md) }= [na + (n2 d- nd) ]

[ma-na] + { m2 d- n2 d } + (nd-md) = 0

a*[m-n] + d* { m2 - n2 } + d* (n-m) = 0

Apply : a2 - b2 = (a+b) (a-b)

a*[m-n] + d* { (m+n) (m-n) } - d* (m - n) = 0

Divide the above equation with " (m-n)" ,We get :

a + d* { (m+n) } - d = 0

a + { (m+n) - 1 } d = 0

COMPARING THE EQUATION WITH : an = a + (n-1) *d

Therefore : a + { (m+n) - 1 } d = am+n

So : am+n = 0

So :the (m+n)th term of the A.P is zero

Answer 2

Answer:

Step-by-step explanation:

He or she is right.