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I was not able to evaluate the following question: What is the sum of the first 20 terms of the geometric sequence $50(1.01)^n$.

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2 Answers

HINT Try geometric series...

$$\sum_{k=0}^{n} ar^k = \frac{a(1-r^{n+1})}{1-r}. $$

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If $\,x, xq, xq^2,...\,$ is a geometric sequence, then

$$S_n=x+xq+xq^2+...+xq^{n-1}=x\frac{q^n-1}{q-1}$$

In your case, $\,x=50(1.01)=50.5\,$ (in case you begin wiht $\,n=1\,$. If you begin with $\,n=0\,$ then $\,x=50\,$) , and $\,q=$...?

Now do the maths

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