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# write an equation to express the geometric sequence 10, 20, 40, 80...

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write an equation to express the geometric sequence 10, 20, 40, 80...

Guest Mar 9, 2017
edited by Guest  Mar 9, 2017
edited by Guest  Mar 9, 2017
edited by Guest  Mar 9, 2017
#1
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x times two

Guest Mar 9, 2017
#2
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Sum =F x (1 - R^N) / (1 - R), where F=First term, R=Common ratio, N=Number of terms.

nth. term =F x R^(N - 1), where F, R and N are the same as above.

Guest Mar 9, 2017
#3
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write an equation to express the geometric sequence 10, 20, 40, 80...

$$\begin{array}{|rcll|} \hline r = \frac{20}{10} = \frac{40}{20} = \frac{80}{40} &=& 2 \\ a&=&10 \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline a_n &=& a\cdot r^{n-1} \\\\ a_n &=& 10\cdot 2^{n-1} \\ \hline \end{array}$$

check:

$$\begin{array}{|rcll|} \hline a_1 &=& 10\cdot 2^0 = 10 \\ a_2 &=& 10\cdot 2^1 = 20 \\ a_3 &=& 10\cdot 2^2 = 40 \\ a_4 &=& 10\cdot 2^3 = 80 \\ a_5 &=& 10\cdot 2^4 = 160 \\ \cdots \\ \hline \end{array}$$

heureka  Mar 9, 2017