Question

Which term of A.P. 121, 117, 113, ... is its first negative term? If it is the nth term, find Sn.

Answer 1

Given A.P. 121, 117, 113.......

a=121 d= 117-121= (-4)

let the nth term of the given AP is 1st negative term then,

n<0

a+(n-1)d < 0

=>121+(n-1)(-4) < 0

=>121-4n+4 < 0

=>125-4n < 0

=>n > -125/-4= 31.25

since the 1st negative term is greater than 31.25

it is 32nd term

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

= 32/2 (2×121+(32-1)(-4)

=16(242+31×-4)

=16× 242-124

= 16×118

= 1888