The no of terms in an ap is even. The sum of odd and even numbered terms are 24 and 30 respt. If the last term exceeds the 1st term by 10 then find no of terms

let the total no.of terms be 2n , & first term ,a & common diff. be d

 a + (2n-1 ) d = l  

& l-a = 10.5 

if we take only the odd terms , it will also be a A.p. of n terms  with common diff. of 2d

24 = n/2 { 2a  + (n-1)2d  }

24 = n { a + (n-1 )d }     .................................(2)

similarly,

30 = n/2 { 2(a+d) + (n-1)2d  }

30  = n/2 { 2a  + 2nd }

30 = n { a + nd }                   ...............................(3)

putting the value of   n { a + nd }  from eq 3  , in eq 2,

24 = 30 - nd

nd = 6 , putting in eq 1

12 - d = 10.5

d = 1.5 , so   n = 6/ 1.5 = 4

putting in eq  3,

30 = 4 ( a + 6 )

 a = 1.5

  so the no. of terms  = 2n = 8

 & series ,

  1.5 ,  3, 4.5 , 6, 7.5, 9, 10.5 . 12