Question

Work out an expression for the nth term for this sequence: 23,35,47,49

Answer 1

Answer:

$a_n = 23 +12(n -1)$

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 $23$ so $a_1 = 23$.

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 $n = 2$

$d = a_2 - a_{2 -1} \\d = a_2 -a_{1} \\d = 35 -23 \\ d = 12$.

Now let's plug everything we know.

$a_1 = 23$

$d = 12$

$a_n = 23 + 12(n -1)$