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Vishrant Vasavada Grade: 11
        The number of terms of an AP is even; the sum of the odd terms is 24, of the even terms is 30, and the last term exceeds the first term by 10.5. Find number of terms and series...
7 years ago

Answers : (1)

Pratham Ashish
17 Points
										

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


 


 


 


 


 



 (2n-1 ) d  = 10.5                     .............. ...............(1)


 

7 years ago
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