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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
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