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# Help please

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An infinite geometric series has common ratio -1/3 and sum 25. What is the second term of the sequence?

Jul 14, 2020

### 2+0 Answers

#1
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The formula for the sum in a infinite geometric sequence is $$\frac{{a}_{1}}{1-r}$$ where a is the first term and r is the common ratio. We know that the sum equals 25 so $$\frac{{a}_{1}}{1-r}=25$$. We also know the common ratio so $$\frac{{a}_{1}}{1+\frac{1}{3}}\Rightarrow\frac{{a}_{1}}{\frac{4}{3}}=25$$. Solve for a and you get $$25\times\frac{4}{3}\Rightarrow\frac{100}{3}$$ but it's asking for the second term (this is the first term) so we multiply $$\frac{100}{3}$$ by $$-\frac{1}{3}$$ (the common ratio) and you get $$-\boxed{\frac{100}{9}}$$

Jul 14, 2020
#2
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That is correct!

Thank you very much :D

Jul 14, 2020