Question

If the 3ʳᵈ and the 9ᵗʰ terms of an AP are 4 and -8 respectively which

term of this AP is zero.​

Answer 1

3ʳᵈ = a+2d = 4 ..........1

9ᵗʰ = a+8d = -8 ..........2

form eq 1 and eq 2

-6d = 12

d = -2

put d to for a

a+ -4 = 4

a= 8

An = a+(n-1)d =

0= 8+ (n-1 ) -2

0= 8 -2n +2

-10 = -2n

n = 5

we get 0 at 5th term

Answer 2

Answer :

5th term is zero.

Step-by-step explanation :

 $\underline{\underline{\bf Arithmetic \ Progression :}}$

• It is the sequence of numbers such that the difference between any two successive numbers is constant.

• In AP,

          a - first term

          d - common difference

          aₙ - nth term

          Sₙ - sum of n terms

•  General form of AP,

             a , a+d , a+2d , a+3d , ..........

•  Formulae :-

              nth term of AP,

                $\boxed{\bf a_n=a+(n-1)d}$

               

               Sum of n terms,

                $\boxed{\bf S_n=\frac{n}{2}[2a+(n-1)d]}$

___________________________

               

Given,

3ʳᵈ term = 4

9ᵗʰ term = -8

• 3rd term = 4

         $a+(3-1)d=4\\\\a+2d=4 \ \ ----(1)$

• 9th term = -8

        $a+(9-1)d=-8\\\\a+8d=-8 \ \ ----(2)$

Subtract eq. (1) from eq.(2)

  a + 8d = -8

(-)a + 2d = 4

_________

      6d = -12

       d = -12/6

       d = -2

⇒ common difference = -2

Substitute the value of 'd' in any equation to get the first term - a;

        a + 2d = 4

        a + 2(-2) = 4

        a - 4 = 4

        a = 4+4

        a = 8

⇒ First term = 8

    we have to find which term is zero,

      let nth term be 0

      a + (n-1)d = 0

      8 + (n-1)(-2) = 0

      8 - 2n + 2 = 0

      10 - 2n = 0

        2n = 10

        n = 10/2

         n = 5

∴ 5th term is zero.