Question

If 3rd and 4th term of an AP are 4 an -8 respectively which term of this AP is zero

Answer 1

Given ,

3rd term is 4

4th term = -8

So ,

a + 2d = 4
a + 3d = -8
==========
-d = 12 .
d = - 12 .

Now put d value in any equation .

a + 2(-12) = 4
a - 24 = 4
a = 4 + 24 = 28 .

Let the n th term be " 0 "

a + ( n - 1 ) -12 = 0
28 - 12n + 12 = 0
40 - 12n = 0
-12n = -40
n = 40/12 = 10/3 .

The term is not a natural number , Hence there might be mistakes in the question.

Solving the question after correcting it ,

If 3rd and 4th term of an AP are 4 and 8 respectively which term of this AP is zero

Answer :
a + 2d = 4
a + 3d = 8
=========
-d = -4
d = 4

=> a + 2(4) = 4
=> a + 8 = 4
=> a = 4 - 8 = -4

So , Let pth term be 0

a + ( p - 1 )d = 0
-4 + ( p - 1 ) 4 = 0
-4 + 4p - 4 = 0
4p - 8 = 0
4p = 8
p = 2 .

Therefore , Second term of this AP is zero.

Answer 2

☺ Hello mate__ ❤

◾◾here is your answer...

It is given that 3rd and ninth term of AP are 4 and -8 respectively.

It means ᵃ₃=4 and a₉=−8 where, a₃ and a9 are third and ninth terms respectively.

Using formula an=a+(n−1)d,   to find nth term of arithmetic progression, we get

4 =  a + (3-1)d    And, -8 = a + (9-1)d

⇒4=a+2d   And, −8=a+8d

These are equations in two variables. Lets solve them using method of substitution.

Using equation 

4=a+2d,

we can say that 

a=4−2d.

Putting value of a in other equation 

−8=a+8d,

we get

−8=4−2d+8d

⇒−12=6d

⇒d=−126=−2

Putting value of d in equation  

−8=a+8d,

we get

−8=a+8(−2)

⇒−8=a−16

⇒a=8

Therefore, first term =a=8    and

Common Difference =d=−2

We want to know which term is equal to zero.

Using formula an=a+(n−1)d,   to find nth term of arithmetic progression, we get

0=8+(n−1)(−2)

⇒0=8−2n+2

⇒0=10−2n

⇒2n=10

⇒n=102=5

Therefore, 5th term is equal to 0.

I hope, this will help you.

Thank you______❤

✿┅═══❁✿ Be Brainly✿❁═══┅✿