Tom and Katie are discussing the sequence: 22, 17, 12, 7, 2 Tom says the nth term rule is: -5n+17
Katie says the nth term rule is: 27-5n

A)Only Tom is correct
B)Only Katie is correct
C)They both are correct
D)Neither are correct

B

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 17 - 22 = 12 - 17 = 7 - 12 = 2 - 7 = - 5

This indicates the sequence is arithmetic with n th term

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 22 and d = - 5, then

= 22 - 5(n - 1) = 22 - 5n + 5 = 27 - 5n → B

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