Question

Find the middle term of the AP 10,7,4,.........(-62). (3 marks)

Answer 1

Hi ,

10 , 7 , 4 , ...... , ( -62 ) are in A.P

first term = a  = 10

common difference = d = a3 - a2 = 4 - 7 = -3

last term = n th term = an = l = - 62

we know that ,

 a + ( n - 1 ) d = l

put above values in the formula,

10 + ( n - 1 ) ( - 3 ) = -62

⇒ ( n- 1 ) ( -3 ) = -62 - 10

⇒ ( n - 1 ) ( - 3 ) = - 72

⇒ ( n - 1) =  ( - 72 ) / ( - 3 )

⇒ n - 1 = 24

∴ n= 24 +1 

   n = 25 

ii ) number of terms in given A. P = n= 25 ( odd )

middle term = ( n+ 1 ) /2 th term

                    = (25 +1) / 2 th term

                    = 26 /2  th term

                     = 13 th term

iii) a = 10 , d= -3 , n= 13 , 

     a13 = ?

     a13 = a + 12d
       
            = 10 + 12 × ( -3 )

            = 10 - 36

            = -26 

∴ middle term in given A. P = a 13 = -26

I hope this helps you.

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Answer 2

if n=odd we need to use formula (n+1)/2.so, we get the middle term.