Question

If s1 is equal to sum of n terms
S2. Is equal to sum of 2n terms
And S3 equal to sum of 3ñ terms
Then prove that.. S3 = 3(S2-S1).

Answer 1

s1 = n/2 (2a + ( n-1 ) d
s2 = 2n/2 (2a + (2n-1)d)
s3 = 3n/2 (2a+(3n-1)d)
solving r.h.s.
3 [ 2n/2 {2a + (2n-1) d} - n/2 { 2a + (n-1)d} ]
3 [n/2 (4a + 4nd - 2d - 2a - dn + d )
3n/2 (2a + 3nd - d )
3n/2 ( 2a + ( 3n -1 ) d )
= L.H.S.

Answer 2

plz refer to this attachment