Question

Which term of Ap 121,117,113,.....,is its first negative term ?

Answer 1

121, 117, 113, ................

First term a = 121

Common difference d = 117-121 = -4

Let nth term is the first negative term in AP

Now nth tern in AP = a + (n-1)*d

= 121 + (n-1)*(-4)

= 121 -4n + 4

= 125 - 4n

Now, we have to find the suitable value of n so that the value of (125 - 4n) is negative.

=> 125 - 4n < 0

=> 124 < 4n

=> 4n > 125

=> n > 125/4

=> n > 31.25

=> n = 32

Now, by taking value of n = 32, we get

nth term = 125 - 4*32

= 125 - 128

= -3

This is the first negative term in the series.

So, n = 32

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