Question

Find the nth terms of the sequence with the following first four terms as shown in the table.

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n 1 2 3 4
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an 5 9 13 17
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Answer 1

see explanation

Explanation:

Both sequences have a common difference between consecutive terms, that is

2 - 1 = 3 - 2 = 4 - 3 = 1

This indicates the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 1 and d = 1 , thus

`a_(n)` = 1 + n - 1 = n

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Similarly

d = 9 - 5 = 13 - 9 = 17 - 13 = 4 and a₁ = 5 , then

`a_(n)` = 5 + 4(n - 1) = 5 + 4n - 4 = 4n + 1