What is the missing term in this geometric sequence ..., -32, __, -128, ...?

1 Answer
Veddesh #phi#
Dec 6, 2016

#color(purple)(-64# or #color(violet)(64#

Explanation:

A geometric sequence is a series in which the number succeeding the first number is got by multiplying the previous number with some fixed ratio, this ratio is known as the common ratio

#color(purple)(-32^(xx2),-64^(xx2),-128^(xx2)....#

The common ratio in this sequence is #2#

So,

#-32*2=color(purple)(-64#

And

#color(purple)(-64)*2=-128#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

But, the common ratio can also be #-2# ans the missing number can be #64#

#color(violet)(-32^(xx-22),64^(xx-12),-128^(xx-2)....#

So,

#-32*-2=color(violet)(64#

And

#color(violet)(64)*-2=-128#

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