Question

If Sn denotes the sum of first n terms of an AP Prove that S30=3(S20-S10)​

Answer 1

Explanation:

S(30) = 30/2 {2a + (30-1)d}

S(30) = 15{ 2a + 29d} -----(1)

S(20) = 20/2 {2a + (20-1)d}

S(20) = 10{ 2a + 19d} ------(2)

S(10) = 10/2 {2a + (10-1)d}

S(10) = 5{2a + 9d} ----(3)

from equation (2) - (3)

S(20) - S(10) = 20a + 190d - 10a - 45d

= 10a + 145d = 5 { 2a + 29d}

3{ S(20) - S(10)} = 15 {2a + 29d} ------(4)

from equation (1) & (4)

S(30) = 3 { S(20) - S(10) }