Question

the sum of how many term of the A.P 14,12,10,.... will be zero​

Answer 1

Answer:

In this A.P. series,first term is a=14

common difference b= 12-14= -2

let the sum of n terms will be zero

we know sum s=n/2{2a+(n-1).b}

=> n/2{2.14+(n-1)(-2)}=0

=> n/2{28-2n+2}=0

=> n/2{30-2n}=0

=> n{15-n}=0

=> 15-n=0

=> n=15

so,sum of 15 terms will be 0

Answer 2

Answer:

$\bigstar{\bold{Number\:of\:terms=15}}$

Step-by-step explanation:

$\Large{\underline{\rm{Given:}}}$

• Sum of the terms is 0

$\Large{\underline{\rm{To\:Find:}}}$

• Number of terms

$\Large{\underline{\rm{Solution:}}}$

➜ Here we have to find the number of terms of the A.P to get a sum of zero.

➜ We know that sum of n terms of A.P is given by,

    $\boxed{S_n=\dfrac{n}{2} (2a_1+(n-1)\times d)}$

   where n = number of terms

    a₁ = first term

    d = common difference

➜ Here,

    First term = 14

    d = 12 - 14 = -2

    Sₙ = 0

➜ Substitute the data,

    0 = n/2 (2 × 14 + (n - 1) × - 2)

    0 = n (28 -2n + 2)

    0 = n (30 - 2n)

    30 - 2n = 0

    2n = 30

      n = 30/2

      n = 15

➜ Hence the number of terms is 15.

    $\boxed{\bold{Number\:of\:terms=15}}$

$\Large{\underline{\rm{Verification:}}}$

➜ Sₙ = 0

    Sₙ = 15/2 ( 2 × 14 + (15 - 1) × -2)

    Sₙ = 7.5 (28 + -28)

    Sₙ = 7.5 × 0

    Sₙ = 0

➜ Hence verified.