Answer: $2,138
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Explanation:
We are summing terms of a geometric sequence with
- a = 100 = first term
- r = 1.10 = common ratio representing 10% increase
To find the sum of the first n terms of a geometric sequence, use this formula
[tex]S_n = \frac{a(1-r^n)}{1-r}\\\\[/tex]
We'll plug in the 'a' and r values mentioned, along with n = 12.
[tex]S_n = \frac{a(1-r^n)}{1-r}\\\\S_{12} = \frac{100(1-(1.10)^{12})}{1-1.10}\\\\S_{12} \approx 2,138.428376721\\\\S_{12} \approx 2,138.43\\\\S_{12} \approx 2,138[/tex]
After 12 months, you have saved about $2,138
