Question

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

Answer 1

A.P : 121, 117, 113...

a = 121

d =  117- 121= -4

Let an= 0

an = a + (n-1)d

⇒ 0 = 121 + (n-1)(-4)

⇒ 0 = 121 - 4n + 4

⇒4n = 125

⇒ n = 125/4

⇒ n = 31.25

n must be natural number therefore n= 32

Hence, 32nd term is first 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