Question

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What is the nth term rule of the linear sequence below?
-9,-5, -1,3,7,...
Tn=

Answer 1

`T_(n)` = 4n - 13

Explanation:

There is a 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

`T_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 9 and d = 4, thus

`T_(n)` = - 9 + 4(n - 1) = - 9 + 4n - 4 = 4n - 13