Question

Which term of the AP:121,117,113,...,is its first negative term

Answer 1

An=a + (n-1)d

a=121. d=117-121=-4. An=0 (suppose)

therefore

0 = 121 + (n-1)×(-4)

n-1)×(-4)= -121

(n-1) =121÷4

n = 125÷4 =31.25=32

so the first negative term is 32



n=

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