Question

The sum of first six terms of ap is zero and the 4th term is 2. Find the sum of its first 30 terms

Answer 1

Answer:

Given S₆ = 0

=> n/ 2 ( 2 a + (n - 1)d) = 0

=> 3 ( 2a + 5d ) = 0

=> 2a + 5d = 0                                     ---------------------A.

Also,

given,

a + 3d = 2                                            -------------------- B.

Multiplying B. by 2 we get ;

2a + 6d = 4                                       -------------------------C.

Solving C. and A. we get;

d = 4 ; a = (-10)

Thus,

S₃₀ = 30 / 2 ( 2 x {-10} + (29)4 )

=> 15 ( -20 +   116)

=> 15 (96)

=> 1440 = S₃₀

Thus, the answer = 1440