Question

If a1 = 6 and an =an-1 -4 then find the value of a4.

Answer 1

Sequences

We know that

`\begin{gathered} a_1_{}^{}=6 \\ a_n=a_(n-1)-4 \end{gathered}`

We want to find a₄, in order to find it we have to find the previous terms:

a₁, a₂, a₃

In order to find a₂ we use the previous term a₁:

`\begin{gathered} a_1=6 \\ a_2=a_(2-1)-4 \\ =a_1-4 \\ =6-4=2_{} \end{gathered}`

Similarly, we find a₃

`\begin{gathered} a_2=2 \\ a_3=a_(3-1)-4 \\ =a_2-4 \\ =2-4=-2 \end{gathered}`

Now we can find a₄, using a₃:

`\begin{gathered} a_3=-2 \\ a_4=a_(4-1)-4 \\ =a_3-4 \\ =-2-4=-6 \end{gathered}`

Answer: a₄ = -6