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`        if the first and (2n_1)th term of an AP,GP andHP are equal and their nth term are a,b,and c respectively,then`
7 years ago

147 Points
```										dear sudhir singh
let first term is x
then (2n-1)th term
x+(2n-2)d1  = xr2n-2 = x/{1+(2n-2)d2} =k

so  (n-1)d1=(k-x)/2
and  rn-1=√k/x
and   x (n-1)d2 =(x-k)/2k

so for nth term
given   a = x+(n-1)d1
=(k+x)/2
b = xrn-1 = √kx
c = x/({1+(n-)d2} = 2kx/(x+k)

clearly   a.c =b2
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7 years ago
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