Question

what is the 13 term of the sequence 2,6,18,54

Answer 1

Notice that:

$\begin{gathered} 2=2\times3^0, \\ 6=2\times3^1, \\ 18=2\times3^2, \\ 54=2\times3^3. \end{gathered}$

Therefore, the rule to compute the nth term of the sequence is:

$a_n=2\times3^{n-1}.$

Substituting n=13 in the above equation we get:

$a_{13}=2\times3^{13-1}=2\times3^{12}=1062882.$

Answer: 1062882.