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Step-by-step explanation:

there is a difference of - 9 between the 3rd and 4th terms. indicating the sequence could be arithmetic , then

a₂ - a₁ = a₃ - a₂ , that is

k - 17 = - 1 - k ( add k to both sides )

2k - 17 = - 1 ( add 17 to both sides )

2k = 16 ( divide both sides by 2 )

k = 8

The sequence is 17, 8, - 1, - 10

The nth term of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 17 and d = - 9 , then

= 17 - 9(n - 1) = 17 - 9n + 9 = 26 - 9n