Question

Which term of AP 129, 125, 121, .... is its first negative term? Give full solutions.


:)

Answer 1

Answer: 34th term is first negative term

Solution:

Given AP is

129,125,121,...

Here a = 129

d= 125-129 = -4

To find the first negative term let us find upto which term this AP gives positive value

place all the values in the nth term formula

$T_{n} < 0 \\ \\ a + (n - 1)d < 0 \\ \\ 129 + (n - 1)( - 4) < 0 \\ \\ - 4(n - 1) < - 129 \\ \\ n - 1 > \frac{129}{4} \\ \\ n > \frac{129}{4} + 1 \\ \\ n > 32.25 + 1 \\ \\ n > 33.25$

So, upto 33.25 terms all terms of AP are positive.

As soon as n will become 34.First negative term of A.P. will appear.

here Notice that n can be integer only.

So,upto 33 term all the terms are positive.

Thus, 34 th term is the first negative term of that AP.

Justification:

$T_{34} = a + 33d \\ \\ = 129 + 33( - 4) \\ \\ = 129 - 132 \\ \\ \bf T_{34}= - 3$

Hope it helps you.

Answer 2

Given A.P is  129, 125, 121, ....

Here, a= 129 and d=121-125=-4

Let nth term be the first negative term.

Then  Tn < 0.

We know,

Nth term of AP is Tn = a + (n - 1)d

=129+(n-1)(-4)

=129-4n+4

=133-4n

Tn < 0

133-4n<0

⇒133<4n

⇒4n>133

N=133/4

33.25

Hence, 34th term will be the first term negative term.