Question

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

Answer 1

The nth term of the given sequence tₙ = 3 n - 7

Explanation:

Given sequence - 4 , -1 , 2 , 5, 8 , .....

First term a = -4

The difference of two terms of a given sequence

d = -1 - (-4) = -1 +4 = 3

d = 2 - (-1) = 2 +1 = 3

d = 5 -2 = 3

d = 8 - 5 =3

The difference of two terms of a given sequence is equal

∴ The given sequence is in Arithmetic progression(AP)

The nth term of given sequence

`t _(n) = a + ( n-1 ) d`

`= -4 + (n -1 ) 3 \\= - 4 + 3n - 3 \\= 3 n - 7`

Final answer:-

The nth term of the given sequence tₙ = 3 n - 7