Question

1 .If Sn denotes the sum of the first n terms of an AP ,Prove that S30=3(S20 – S10).

Answer 1

Sn= n/2[2a +(n-1)d

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

= 15[2a + 29d]

=30a + 435d.................................... eq 1

3[S20-S10]= 3 [ 10{2a + 19d} - 5{2a+9d}

= 3 [ 20a +190d- 10a -45d]

=3 [ 10a +145d]

= 30a + 435 d...................................eq 2

eq 1= eq 2

Therefore, S30=3( S20- S10)

Hope it helped.:-)