How do you find the common ratio for $64,-32,16,-8,4,...$ ?

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Answer 1 · 2016-09-21T12:08:44

Common ratio is $-1/2$

In a Geometric series, common ratio is the ratio of a term with respect to its preceding term.

Here we have the series ${64,-32,16,-8,4,.................}$

and hence common ratio is $-32/64=16/(-32)=-8/16=4/(-8)=-1/2$

Answer 2 · 2016-09-21T12:14:03

Common ratio: $color(green)(-1/2)$

Let the ratio between successive terms $a_n$ and $a_(n+1)$ be $r_n=(a_(n+1))/(a_n)$

Then for the given terms: $64,-32,16,-8,4, ...$
$color(white)("XX")r_1=(-32)/64 = -1/2$

$color(white)("XX")r_2=16/(-32) = -1/2$

$color(white)("XX")r_3=(-8)/16= -1/2$

$color(white)("XX")r_4=4/(-8) = -1/2$

assuming this pattern holds for subsequent (unspecified) terms,
we can see that there is a common ration of $(-1/2)$

How do you find the common ratio for 64,-32,16,-8,4,...64,-32,16,-8,4,...?