Question

For an AP show that tm+tm+2n=2tm+n?

Answer 1

tm+n+tm-n

= [ t + (m+n-1)d ] +[ t + (m-n-1)d ]

= 2t + d(m+n-1 + m-n-1)

= 2t + d(2m-2)

= 2[ t + d(m-1)]

= 2tm

= RHS