以下是一个数列的前四项。 4 12 36 108

1. Continue the sequence by multiplying by the common ratio

The sequence is
$4,\ 12,\ 36,\ 108,\ldots$
Each term is multiplied by $3$.

5th term: $108\times 3=324$

6th term: $324\times 3=972$

1. Identify the common ratio and form the nth term

The sequence is multiplied by $3$ each time.

For a geometric sequence,
$T_n=\text{first term}\times (\text{common ratio})^{n-1}.$

So
$T_n=4\times 3^{n-1}.$

1. Use the nth term expression to set up the check

From part (b), the nth term is
$4\times 3^{n-1}$.

If $16211$ is a term, then
$4\times 3^{n-1}=16211.$

2. Show that no positive integer value of $n$ gives $16211$

Since every term has the form $4\times 3^{n-1}$, every term must be divisible by $4$.

But
$16211\div 4=4052.75,$
which is not an integer.

Therefore $16211$ cannot be a term of the sequence.