Question

If a1=4 and an = an-1 - 4 then find the value of a6.

Answer 1

For the information given in the statement you have

`a_n=a_(n-1)-4`

Then

`\begin{gathered} a_2=a_1-4 \\ a_2=4-4 \\ a_2=0 \end{gathered}`
`\begin{gathered} a_3=a_2-4 \\ a_3=0-4 \\ a_3=-4 \end{gathered}`

That is, to find the nth term, use the immediately previous term already found

`\begin{gathered} a_4=a_3-4 \\ a_4=-4-4 \\ a_4=-8 \end{gathered}`
`\begin{gathered} a_5=a_4-4 \\ a_5=-8-4 \\ a_5=-12 \end{gathered}`

Therefore, the sixth term of the sequence is

`\begin{gathered} a_6=a_5-4 \\ a_6=-12-4 \\ a_6=-16 \end{gathered}`