Question

Finding the first terms of the sequence using recursive rule

Answer 1

Given:

`a_1=6,a_n=-2a_(n-1),n\ge2`

Step 1:

The first term of the sequence will be

`a_1=6`

Step 2:

To figure out the value of the second term, we will have to put the value of n=2

`\begin{gathered} a_n=-2a_(n-1), \\ a_2=-2a_(2-1)=-2a_1 \\ a_2=-2(6) \\ a_2=-12 \end{gathered}`

Hence,

The second term of the sequence will be

`a_2=-12`

Step 3:

To figure out the value of the third term, we will have to put the value of n=3

`\begin{gathered} a_n=-2a_(n-1),n=3 \\ a_3=-2(a_(3-1)) \\ a_3=-2a_2,a_2=-12 \\ a_3=-2(-12) \\ a_3=24 \end{gathered}`

Hence,

The third term of the sequence will be

`a_3=24`

Step 4:

To figure out the value of the fourth term, we will have to put the value of n=4

Hence,

The first four terms of the sequence are 6, -12, 24, -48