If S n denotes the sum of first n terms of an A.P., prove that S 30 = 3(S 20 - S 10 ).

By formula S n = We need to prove S 30 = 3(S 20 - S 10 ). ∴ L.H.S. = R.H.S. = 30a + 335d. Hence, proved that S 30 = 3(S 20 - S 10 ).

The sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is 1 : 3. Calculate the first and the thirteenth term.