Write the explicit equation
for the sequence
9, 5, 1, -3, -7…

= 13 - 4n

Step-by-step explanation:

Note the common difference d between consecutive terms, that is

d = 5 - 9 = 1 - 5 = - 3 - 1 = - 7 - (- 3) = - 4

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 = 9 and d = - 4, thus

= 9 - 4(n - 1) = 9 - 4n + 4 = 13 - 4n ← explicit equation

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