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Given u1 = 56 and un = 0.7un-1, find S12. Round to the nearest hundredth A) 181.39 B) 184.08 C) 185.32 D) 186.66

User Jmancuso
by
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1 Answer

7 votes

Answer:

184.08

Explanation:


u_(1),u_(2),u_(3).....u_(n) form a sequence exhibiting the following property :


u_(1)=56;u_(n)=0.7u_(n-1)

On rewriting,
(u_(n))/(u_(n-1))=0.7Ratio of consecutive terms is a constant. Hence, the sequence is a Geometric Progression.

The ratio
0.7 is the common ratio
r. First term =
a=
u_(1)=56.

Sum of
n terms of a Geometric progression is given by


S_(n)=a*(1-r^(n))/(1-r) when
r<1.


S_(12)=56*((1-(0.7)^(12))/(1-0.7))=56*(0.986)/(0.3)=184.083


S_(12) to the nearest hundreth is 184.08

User Jacob Jennings
by
8.3k points
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