Question

Which term of AP 25,20,15,.... is the first negative term?​

Answer 1

Answer:

The 7th term is the first negative term.

Step-by-step explanation:

In the given question,

We can conclude that the first term

a = 25

And the common difference(d)

d = 20-25

d = - 5

For finding the A. P. :-

We can use the formula

An = a+(n-1)d

As we know:-

For the first negative term it should be less than 0.

So the required equation will be :

=> a+(n-1)d<0

=> 25+(n-1)*(-5)<0

=> (n-1)*(-5)<-25

=>(n-1)>5

=> n>6

Therefore-:

The first negative term is it's 7th term.

Answer 2

GIVEN

The A.P. is 25,20,15....

The First Term, a = 25

The Common Difference, d = -5

an < 0

TO FIND:- 'n' (Term Number of 1st Negative term of the given A.P.)

SOLUTION

The General Term of an Arithematic Progression (A.P.) is given by Tn

=> Tn = a + (n - 1)d

=> Tn < 0 { Applying Given Condition }

=> a + (n - 1)d < 0

=> 25 + (n - 1) -5 < 0 {Solving Inequality}

=> (n - 1)(-5) < - 25

=> n - 1 > 5

=> n > 6 (ANS)

Hence the 7th Term of this Given A.P. will be negative.

VERIFICATIONS

Tn = a + (n - 1)d

=> T5 = 25 + 6d

=> T5 = 25 + 6 × -5

=> T5 = 25 - 30

=> T5 = -5 (Which is first Negative term of this series)

Hence, verified.