Question

which term of an A.P 121,117,113........is the first negative term and first second negative term

Answer 1

a = 121
d = 117-121 = (-4)
let an = 0
so,
an = a+(n-1)d
0 = 121+(n-1)(-4)
-121 = (n-1)(-4)
-121/-4 = n-1
n = (121/4)+1
n = 30.25+1
n = 31.25
but n cannot be in fraction
so, n = 32
so,
a32 = a+31d = 121+31(-4) = 121-124 = -3
so,
-3 is the first negative number and -7 is the second negative number

Answer 2

a = 121

d = -4

let an= 0

then

an = a + (n-1)d

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

=> 0 = 121 - 4n + 4

=> 4n = 125

=> n = 125/4

=> n = 31.25

as n must be natural number then n= 32

32nd term is First negative number.

a32 = 121 + (31)-4

= 121 - 124 = -3