Question

If the 3rd and the 9th term of an ap are 4 and -8 respectively, which term of it is zero?

Answer 1

3rd term of A.P = 4
therefore a+2d = 4→1
9th term of A.P = -8
therefore a+8d = -8→2
On subtracting 2 from 1
a+2d = 4
-(a+8d = -8)
⇒a+2d = 4
   -a - 8d = 8
⇒ -6d = 12
d = -2
On substituting the value of d in a+2d = 4 we get a = 8
let 0 be the last term of the A.P
therefore a+(n-1)d = 0
⇒ 8 + (n-1)-2 = 0
8-2n+2 = 0
⇒-2n = -10
n = 5
therefore 5th term of the A.P is 0

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______❤

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