一个数列的前四项分别是 27，24，21 和 18。

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完整解法

1. Find the common difference and continue the sequence to the 8th term.

The sequence decreases by $3$ each time:

$27,\ 24,\ 21,\ 18,\ 15,\ 12,\ 9,\ 6$

So the 8th term is $6$ .

答案

$6$

1. Find the common difference and form the nth term.

The sequence is $27, 24, 21, 18, \ldots$

Common difference:
$24-27=-3$

Using $T_n=a+(n-1)d$ ,
$T_n=27+(n-1)(-3)$
$T_n=27-3n+3=30-3n$

答案

$30-3n$

1. Check whether $-31$ can be produced by the nth term formula.

From part (b), the nth term is $30-3n$ .

Set it equal to $-31$ :
$30-3n=-31$
$-3n=-61$
$n=\frac{61}{3}$

Since $\frac{61}{3}$ is not a positive integer, $-31$ is not a term in the sequence.

答案

No, since $30-3n=-31$ gives $n=\dfrac{61}{3}$ , which is not an integer.

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