Question

Write the first five terms of each sequence a(1) = 7, a(n) = a(n - 1) - 3 for n = 2.

Answer 1

7 , 4, 1, -2 and -5

Step-by-step explanation:

Given a sequence such that:

`\begin{gathered} a(1)=7 \\ a(n)=a(n-1)-3,n\geqslant2 \end{gathered}`

`\begin{gathered} a\left(2\right)=a\left(2-1\right)-3=a(1)-3=7-3=4\implies a(2)=4 \\ a\left(3\right)=a\left(3-1\right)-3=a(2)-3=4-3=1\implies a(3)=1 \\ a\left(4\right)=a\left(4-1\right)-3=a(3)-3=1-3=-2\implies a(4)=-2 \\ a\left(5\right)=a\left(5-1\right)-3=a(4)-3=-2-3=-5\implies a(5)=-5 \end{gathered}`

Therefore, the first five terms of the sequence are:

7 , 4, 1, -2 and -5