Question

What is the nth term rule of the linear sequence below?
−
4
,
−
1
,
2
,
5
,
8
,
.
.
.

Answer 1

just keep adding 3

and stop typing your text vertically ...

Answer 2

n = 1 , a1 = - 4

n = 2 , a2 = - 1

a2 - a1 = - 1 - ( - 4 ) = - 1 + 4 = 3

n = 3 , a3 = 2

a3 - a2 = 2 - ( - 1 ) = 2 + 1 = 3

n = 4 , a4 = 5

a4 - a3 = 5 - 2 = 3

n = 5 , a4 = 8

a5 - a4 = 8 - 5 = 3

an = a( n -₋1 ) + 3

OR

n = 1 , a1 = - 4 = 3 ∙ n - 7 = 3 ∙ 1 - 7 = 3 - 7

n = 2 , a2 = - 1 = 3 ∙ n - 7 = 3 ∙ 2 - 7 = 6 - 7

n = 3 , a3 = 2 = 3 ∙ n - 7 = 3 ∙ 3 - 7 = 9 - 7

n = 4 , a4 = 5 = 3 ∙ n - 7 = 3 ∙ 4 - 7 = 12 - 7

n = 5 , a4 = 8 = 3 ∙ n - 7 = 3 ∙ 5 - 7 = 15 - 7

You can write a recursive relation:

an = a( n -₋1 ) + 3

Or you can also write a linear relation:

an = 3 n - 7