9514 1404 393
Answer:
453.32
Step-by-step explanation:
The argument of the summation symbol is recognizable as the general term of a geometric series with first term a1=4 and common ratio r=1.5. The indices on the summation symbol tell you that you want the sum of the first 10 terms of the series.
The general form of the sum of the first n terms of a geometric series is ...
Sn = a1(r^n -1)/(r -1)
For the given values of a1 and r, this sum is ...
[tex]S_{10}=4\cdot\dfrac{1.5^{10}-1}{1.5-1}=4\cdot\dfrac{57.6650390625-1}{0.5}\\\\\boxed{S_{10}\approx453.32}[/tex]
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Your graphing calculator may be able to evaluate this for you directly.
