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

x times two

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.

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:

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