Question

find the middle term of the ap 213,205,197,.....,37.

Answer 1

Hi,

Here is your answer,

Given data,

A.P = 213, 205, 197,..............., 27

So, here a1(first term) = 213 and an = 27 (last term) and d(common difference) = 205 - 213 = -8

          an = 27

Formula = a + (n -1 )d

   =  213 + ( n -1) -8 = 37
 
   = 213 - 37 = 8(n-1)

   = 176 = 8(n-1)

   = 176/8 = (n-1)

    = (n-1) = 22

  So, therefore n = 23 

Now,  a₁₂ =  a₁ + 11d

      = -213  + 11 × -8 

      = 213 - 88 = 125


∴  a₁₂ = 125.