Question

If Sn denotes the sum of first n terms of an A.P., prove that, S30 = 3(S20-S10)

Answer 1

Sol:-
Let sum of the first n terms of an A.P, Sn = ( n / 2) [ 2a + ( n -1)d ]

Now S30 = ( 30 / 2) [ 2a + ( 30 -1)d ] ---------(1)

S20 - S10 = ( 20 / 2) [ 2a + ( 20 -1)d ] - ( 10 / 2) [ 2a + ( 10 -1)d ]

S20 - S10 = 10 [ 2a + ( 20 -1)d ] - 5 [ 2a + ( 10 -1)d ]

S20 - S10 = 10a + 190d  -  45d .

3(S20 - S10 ) = 3(10a + 145d )

3(S20 - S10 ) = 3 x 5(2a + 29d )

3(S20 - S10 ) = ( 30 / 2) [ 2a + ( 30 -1)d ] --------(2)

From (1) and (2) we get

S30 = 3(S20 - S10 )

Answer 2

Step-by-step explanation:

Here is the answer in the attachment..