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If x, y, z are the mth, nth and pth terms, respectively of a G.P. then (n – p) log x + (p − m) log y + (m − n) log z =?

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Let the G.P. be 1, 3, 9, 27, 81,…

Let m =2, n =3, p= 5 then (n – p) log x + (p − m) 

log y + (m − n) log z = (3 − 5)log 3 + (5 − 2)log 9 + (2 − 3)log 81 = −2log3 + 6 log 3 − 4log 3 = 0

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