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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
```

6 years ago

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```										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
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin

```
6 years ago

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