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Work out an expression for the nth term for this sequence:

23,35,47,49

Sagot :

Happil

Answer:

[tex]a_n = 23 +12(n -1)[/tex]

Explanation:

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

From the given first five terms of the sequence we can see that the first term is [tex]23[/tex] so [tex]a_1 = 23[/tex].

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

[tex]d = a_2 - a_{2 -1} \\d = a_2 -a_{1} \\d = 35 -23 \\ d = 12[/tex].

Now let's plug everything we know.

[tex]a_1 = 23[/tex]

[tex]d = 12[/tex]

[tex]a_n = 23 + 12(n -1)[/tex]

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