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Work out the nth of this sequence:

Work out the nth of this sequence:-example-1

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Answer:


a_n = -11 +3(n -1)

Step-by-step explanation:

The
nth 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)

User Lazar Nikolic
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