Question

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

Answer 1

S(n) = n/2 × ( 2a + (n-1)d) = (2an + d(n^2) - nd)/2

S(n-1) = (n-1)/2 × ( 2a + (n-2)d) =

( 2an + (n^2)d - 2a + 2d - 3nd)/2

S(n-2) = (n-2) × ( 2a + (n-3)d) =

(2an +(n^2)d - 5nd - 4a + 6d)/2

now filling in equation
S(n) - 2S(n-1) + S(n-2)

the calculation further is showed in pic

Answer 2

Answer: check the attachment

Hope it helps you!!