Question

Identify the explicit function for the sequence in the table x 1,2,3,4,5 y 9,14,19,24,29

Answer 1

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Answer 2

`a_(n)` = 5n + 4

Explanation:

There is a common difference between the consecutive terms of y

29 - 24 = 24 - 19 = 19 - 14 = 14 - 9 = 5

This indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 9 and d = 5 , then

`a_(n)` = 9 + 5(n - 1) = 9 + 5n - 5 = 5n + 4