Question

Finding the first terms of the sequence using recursive rule

Answer 1

Answer:

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

$undefined$

Hence,

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