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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...
8 years ago

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)

8 years ago
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