Question

Work out the nth of this sequence:

Answer 1

Answer:

$a_n = -11 +3(n -1)$

Explanation:

The $n$th term of an arithmetic sequence is explicitly defined as $a_n = a_1 +d(n -1)$ where $a_1$ is the first term of the sequence and $d$ is the the common difference.

From the given first five terms of the sequence we can see that the first term is $11$ so $a_1 = 11$.

The common difference, $d$, can be calculated by $a_n - a_{n -1}$ so we'll find the common difference of the given sequence by letting $n = 2$

$d = a_2 - a_{2 -1} \\d = a_2 -a_{1} \\d = -8 -(-11) \\ d = -8 +11 \\ d = 3$.

Now let's plug everything we know.

$a_1 = -11$

$d = 3$

$a_n = -11 +3(n -1)$