Question

2. In an A.P. the 4th term is 17 and 7th term is 23.Find25th term​

Answer 1

Step-by-step explanation:

hope the above two photos helps you sister......

Answer 2

Answer:

$\bigstar{\bold{The\:25th\:term\:of\:the\:A.P=59}}$

Step-by-step explanation:

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

• The fourth term of the A.P is 17
• The seventh term of the A.P is 23

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

• The 25th term of the A.P

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

→ The fourth term of an A.P is given by,

  a₄ = a₁ + 3d

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

→ By given,

  a₁ + 3d = 17----(1)

→ The 7th term of an A.P is given by

  a₇ = a₁ + 6d

→ By given,

  a₁ + 6d = 23 ------(2)

→ Solve equation 1 and 2 by elimination method,

  a₁ + 6d = 23

  a₁ + 3d = 17

         3d = 6

           d = 6/3

           d = 2

→ The common difference of the A.P is 2.

→ Substitute the value of d in equation 1

  a₁ + 3 × 2 = 17

  a₁ + 6 = 17

  a₁ = 17 - 6

  a₁ = 11

→ The first term of the A.P is 11

→Now we have to find the 25th term which is given by

 a₂₅ = a₁ + 24d

→ Substitute the data,

  a₂₅ = 11 + 24 × 2

  a₂₅ = 11 + 48

  a₂₅ = 59

→ Hence the 25th term of the A.P is 59

  $\boxed{\bold{The\:25th\:term\:of\:the\:A.P=59}}$

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

→ The nth term of an A.P is given by

   $\sf{a_n=a_1+(n-1)\times d}$

→ The common difference is given by

   $\sf{d=a_2-a_1}$

  $\sf{d=\dfrac{a_m-a_n}{m-n} }$