Question

prove SN- 2SN-1 + Sn-2 = d, for an AP where first term is a & common diff. is d

Answer 1

just replace Sn-1 by Sn - An
replace Sn-2 by Sn- An - An-1
then everything will cancil out and you will get
An- An-1 = d
and offcourse difference between 2 terms is d