Let a be the first term and r be the common ratio of the given GP. Then,

`T_(m)=ar^((m-1)), T_(n)=ar^((n-1))` and `T_(p)=ar^((p-1))`.

Since, `T_(m), T_(n), T_(p)` are in GP, we have

`T_(n)^(2)=T_(m)xxT_(p)`

`rArr [ar^((n-1))]^(2)=[ar^((m-1))xxar^((p-1))]`

`rArr a^(2) r^((2n-1))=a^(2)r^((m+p-2))`

`rArr r^((2n-2))=r^((m+p-2))`

`rArr 2n-2=m+p-2`

`rArr 2n=m+p rArr m, n, p` are in AP.

Hence, m, n, p are three consecutive terms of an AP.