Question

if the 5th and 15th term of an a.p are 20 and -20 then which term of this a.p is zero​

Answer 1

Answer:

$\bigstar{\bold{10th\:term\:of\:the\:A.P=0}}$

Step-by-step explanation:

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

• The fifth term of the A.P (a₅) = 20
• The fifteenth term of the A.P = -20

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

• Which term of the A.P is 0?

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

⇝ First we have to find the first term and common difference of the A.P

⇝ The fifth term of an A.P is given by

    a₅ = a₁ + 4d

    a₁ + 4d = 20-------(1)

⇝ The fifteenth term of an A.P is given by

    a₁₅ = a₁ + 14d

    a₁ + 14d = -20-------(2)

⇝ Solving equation 1 and 2 by elimination method

    a₁ + 14d = -20

    a₁ + 4d = 20

           10d = -40

               d = -40/10

               d = -4

⇝ Hence common difference of the A.P is -4.

⇝ Substitute the value of d in equation 1

    a₁ + 4 × - 4 = 20

    a₁ + -16 = 20

    a₁ = 20 + 16

    a₁ = 36

⇝ Hence the first term of the A.P is 36

⇝ Now we have to find out which term of the A.P is 0

⇝ $\sf{a_n=a_1+(n-1)\times d}$

    where $a_n$ = 0, a₁ = 36, d = -4

⇝ Substitute the datas,

    0 = 36 + (n - 1) × - 4

    0 = 36 + -4n + 4

    0 = 40 + -4n

    -4n = -40

       n = 40/4

       n = 10

⇝ Hence the 10th term of the A.P is 0.

    $\boxed{\bold{10th\:term\:of\:the\:A.P=0}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

⇝ The nth term of the A.P is given by,

    $\sf{a_n=a_1+(n-1)\times d}$

⇝ The common difference of an A.P is given by,

    $\sf{d=a_2-a_1}$

    $\sf{d=\dfrac{a_m-a_n}{m-n} }$