Question

find 9th A.P when 4th A.P is 5 and 8th A.P is 15.

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Answer 1

Answer:

the 9th term of the AP is 35/2

Step-by-step explanation:

a = -5/2

d = 5/2

Answer 2

Answer:

$\bigstar{\bold{Ninth\:term\:of\:the\:A.P=\dfrac{85}{7}}}$

Step-by-step explanation:

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

• The 4th term of the A.P = 5
• The 8th term of the A.P = 15

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

• The 9th term of the A.P

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

⇝ Let us assume the first term of the A.P as a₁ and the common difference as d.

⇝ We know the nth term of an A.P is given by,

    $\sf a_n=a_1+(n-1)\times d$

    where a₁ is the first term and d is the common difference

⇝ Hence fourth term of the A.P is given by,

    a₄ = a₁ + 3d

⇝ But by given the fourth term is 5.

    a₁ + 3d = 5-----(1)

⇝ Also eight term of the A.P is given by,

    a₈ = a₁ + 7d

⇝ By given eighth term of the A.P is 8.

    a₁ + 7d = 15-----(2)

⇝ Solving equation 1 and 2 by elimination method,

    a₁ + 7d = 15

    a₁ + 3d = 5

           7d = 10

             d = 10/7

⇝ Hence the common difference of the A.P is 10/7.

⇝ Now substitute the value of d in equation 1,

   a₁ + 3 × 10/7 = 5

   a₁ = 5 - 30/7

   a₁ = (35 - 30)/7

   a₁ = 5/7

⇝ Hence first term of the A.P is 5/7.

⇝ Now finding the ninth term.

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

    a₉ = a₁ + 8d

    a₉ = 5/7 + 8 × 10/7

    a₉ = (5 + 80)/7

    a₉ = 85/7

   a₉ = 85/7

⇝ Hence the ninth term of the A.P is 85/7.

    $\boxed{\bold{Ninth\:term\:of\:the\:A.P=\dfrac{85}{7}}}$