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