Question

Write the first five terms of the sequence defined by the recursive formula an=an-1/2-1, with a1=1

Answer 1

Given first term a1 = 1 and the recursive formula is given:

`a_n=(a_(n-1))/(2)-1`

We have to find the next four terms of the sequence.

The second term is:

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

The third term is :

`\begin{gathered} a_3=(a_(3-1))/(2)-1 \\ =(a_2)/(2)-1 \\ =((-1)/(2))/(2)-1 \\ =-(1)/(4)-1 \\ =-(5)/(4) \end{gathered}`

The fourth term is:

`\begin{gathered} a_4=(a_(4-1))/(2)-1 \\ =(a_3)/(2)-1 \\ =((-5)/(4))/(2)-1 \\ =-(5)/(8)-1 \\ =-(13)/(8) \end{gathered}`

The fifth term is:

`\begin{gathered} a_5=(a_(5-1))/(2)-1 \\ =((-13)/(8))/(2)-1 \\ =-(13)/(16)-1 \\ =-(29)/(16) \end{gathered}`

Thus, option D is correct.