Geometric Series

​Geometric Series

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​Geometric Series

Multiple Choice

What is the sum of 1st 5 terms of the geometric sequence where first term is 5 and common ratio is 2?

$$a_n=\frac{a_1\left(1-r^n\right)}{1-r}$$  

• 155

• -155

• 150

• -150

​What is the sum of 1st 5 terms of the geometric sequence where first term is 5 and common ratio is 2?

Multiple Choice

Find the sum of the 1st 12 terms of 3, -9, 27, -81, ...

$$S_n=\frac{a_1\left(1-r^n\right)}{1-r}$$  

• -398,580

• 398,580

• 580,398

• -580,398

​Find the sum of the 1st 12 terms of 3, -9, 27, -81, ...

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​Infinite Geometric Series

Multiple Choice

Identify the series if divergent or convergent.

$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...$$  

• divergent

• convergent

​Identify if the series is divergent or convergent

Multiple Choice

Identify if the series is divergent or convergent.

$$2+\left(-6\right)+12+\left(-24\right)+...$$  

• divergent

• convergent

​Identify if the series is divergent or convergent

Multiple Choice

Compute for the sum of the series

$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...$$  

$$S_{\infty}=\frac{a_1}{1-r}$$  

• $$\frac{-1}{2}$$  

• $$-2$$  

• $$\frac{1}{2}$$  

• $$2$$  

​Compute for the sum of the series

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