Answer: 2.325
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Work Shown:
The shortcut way to do this is to plug a = 1.2, r = 0.5 and n = 5 into the formula below.
[tex]S_n = \frac{a*(1-r^{n})}{1-r}\\\\S_{5} = \frac{1.2*(1-0.5^{5})}{1-0.5}\\\\S_{5} = \frac{1.2*(1-0.03125)}{1-0.5}\\\\S_{5} = \frac{1.2*(0.96875)}{0.5}\\\\S_{5} = \frac{1.1625}{0.5}\\\\S_{5} = 2.325\\\\[/tex]
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The longer way is to generate the first five terms, then add them up. To generate the terms, we multiply each term by 0.5 to get the next one.
a1 = first term = 1.2
a2 = second term = 0.6, result of multiplying 0.5 and 1.2
a3 = third term = 0.3
a4 = fourth term = 0.15
a5 = fifth term = 0.075
Now add up the five terms
a1+a2+a3+a4+a5 = 1.2+0.6+0.3+0.15+0.075 = 2.325
This method isn't too tedious since n = 5 isn't too large. For large values of n, it is better to use the formula shown in the previous section.
