What is the sum of the geometric sequence 1, 3, 9, ... if there are 14 terms?
+26396 What is the sum of the geometric sequence 1, 3, 9, ... if there are 14 terms?
\small{\text{ geometric sequence: $a_1 = 1 \quad r = 3$ }}\\ \small{\text{ $ \begin{array}{lcll} \hline \\ s_{14} &=& \textcolor[rgb]{150,0,0}{1} + & 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 3^7 + 3^8 + 3^9 + 3^{10} + 3^{11} + 3^{12} + 3^{13} \\ 3\cdot s_{14} &=& & 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 3^7 + 3^8 + 3^9 + 3^{10} + 3^{11} + 3^{12} + 3^{13} + \textcolor[rgb]{150,0,0}{3^{14}}\\ \hline \\ s_{14}-3\cdot s_{14} &=& \textcolor[rgb]{150,0,0}{1-}&\textcolor[rgb]{150,0,0}{3^{14}}\\ s_{14}\cdot(1-3) &=& 1- &3^{14}\\ -2\cdot s_{14} &=& 1- &3^{14}\\ \end{array} $}}
s14=1−314−2s14=314−12=2391484
+26396 What is the sum of the geometric sequence 1, 3, 9, ... if there are 14 terms?
\small{\text{ geometric sequence: $a_1 = 1 \quad r = 3$ }}\\ \small{\text{ $ \begin{array}{lcll} \hline \\ s_{14} &=& \textcolor[rgb]{150,0,0}{1} + & 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 3^7 + 3^8 + 3^9 + 3^{10} + 3^{11} + 3^{12} + 3^{13} \\ 3\cdot s_{14} &=& & 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 3^7 + 3^8 + 3^9 + 3^{10} + 3^{11} + 3^{12} + 3^{13} + \textcolor[rgb]{150,0,0}{3^{14}}\\ \hline \\ s_{14}-3\cdot s_{14} &=& \textcolor[rgb]{150,0,0}{1-}&\textcolor[rgb]{150,0,0}{3^{14}}\\ s_{14}\cdot(1-3) &=& 1- &3^{14}\\ -2\cdot s_{14} &=& 1- &3^{14}\\ \end{array} $}}
s14=1−314−2s14=314−12=2391484
