Question

What is the sum of the first five terms of a geometric series with a_1 = 6 and r = 1/3?

Answer 1

Using the formula..
\[\sum_{k=0}^{n-1} (ar^k) = a \frac{ 1-r^n }{ 1-r }\]

Answer 2

so..
\[6 \times \frac{ 1-(1/3)^5 }{ 1-1/3 }\]
is this set up correctly?

Answer 3

\[6 \times \frac{ 242/243 }{ 2/3 }\]
\[6 \times \frac{ 242 }{ 243 } \times \frac{ 3 }{ 2 }\]

Answer 4

\[6 \times \frac{ 121 }{ 81 }\]

Answer 5

\[\frac{ 726 }{ 81 }\]
is this the answer..