Question

The sum of 2n terms of

a.P. {1, 5, 9, 13…..} is greater than sum of n terms of

a.P. = {56, 58, 60..…}. What is the smallest value n can take?

Answer 1

A.P.(1) ; 1,5,9,13...( where a= 1 & d = 4 )
A.P.(2); 56,58,60....( where a1 = 56 & d1 = 2 )
A.T.Q.-
Sn(1)›Sn(2)
n/2 ( 2a + (n-1)d ) › n/2 ( 2a1 +(n-1) d1)
2(1) + (n - 1) (4) › 2(56) + (n - 1) (2)
2 + 4n - 4 › 112 + 2n - 2
4n -2 › 110 + 2n
2n › 112
n › 56
Therefore; n › 56