Answer:
see explanation
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
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 17 and d = - 9 , then
[tex]a_{n}[/tex] = 17 - 9(n - 1) = 17 - 9n + 9 = 26 - 9n
