Question

if the sum of first and two and three and term of an ap S1 ,S2 and S3 respectively then prove that S3 = 3 (S2 - S1)

Answer 1

Yes i am doing on page

We know that S3 = N/2 ( 2a +(n-1)d)
S3 = 3/2 ( 2a +( 3-1)d)
S3 = 3/2 ( 2a + 2d)
S3 = 3a + 3d


Also 3 ( S2 - S1 )

3 ( N/2 ( 2a +( n-1)d) - ( 2a + (n-1)d )

3 ( 2/2 ( 2a+(2-1)d) -1/2(2a + ( 1-1)d)

3 ( 1 ( 2a +d) -1/2( 2a + 0d)

3( 2a +d - 1a-0d)
3 ( 1a +1d)
3a+3d

Both answer are same therefore proved.