Given that a,b,c are 3 consecutive term of a Geometric sequence f(n) , show that log a,logb,logc are the first 3 terms of an Arithmetic SequenceP(n).


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Question Number 38154 by Rio Mike last updated on 22/Jun/18

$G i v e n t h a t$ $a, b, c a r e 3 c o n s e c u t i v e t e r m o f$ $a G e o m e t r i c s e q u e n c e f (n), s h o w$ $t h a t l o g a, l o g b, l o g c a r e t h e f i r s t$ $3 t e r m s o f a n A r i t h m e t i c S e q u e n c e P (n) .$
	Answered by Rasheed.Sindhi last updated on 22/Jun/18

	$a, b = a r, c = {a r}^{2}$ $l o g a, l o g b = l o g a r = l o g a + l o g r$ $l o g c = l o g ({a r}^{2}) = l o g a + 2 l o g r$ $(i) l o g b - l o g a = l o g a + l o g r - l o g a = l o g r$ $(i i) l o g c - l o g b = (l o g a + 2 l o g r) - (l o g a + l o g r)$ $= l o g r$ $F r o m (i) & (i i)$ $l o g b - l o g a = l o g c - l o g b = l o g r$ $∴ l o g a, l o g b & l o g c a r e i n A P$
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