How do you write the explicit formula for the following geometric sequence: -0.1, 0.03, -0.009, 0.0027, -0.00081, ...?

1 Answer
Shwetank Mauria
Sep 13, 2016

#n^(th)# term of given geometric series is #(-0.1)xx(-0.3)^(n-1)#

Explanation:

In the given geometric series

#{-0.1,0.03,-0.009,0.0027,-0.00081,......}#,

the first term is #-0.1# and common ratio is #0.03/(-0.1)=(-0.009)/0.03=0.0027/(-0.009)=(-0.00081)/0.0027=-0.3#

As the #n^(th)# term of a geometric series whose first term is #a# and common ratio is #r# is #axxr^(n-1)#

Hence #n^(th)# term of given geometric series is

#(-0.1)xx(-0.3)^(n-1)#

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