Question

Suppose that a sequence is defined as follows. 2. =-1, 2,=-3a,-1+6 for 122 List the first four terms of the sequence.

Answer 1

the first term is a1 = -1

the given expression is

$a_n=-3a_{n-1}+6\text{ for n}\ge2$

put n = 2

$\begin{gathered} a_2=-3a_{2-1}+6 \\ a_2=-3a_1+6 \\ a_2=-3\times-1+6=3+6=9 \\ \end{gathered}$

so the second term is a2 = 9

for the third term, put n = 3

$\begin{gathered} a_3=-3a_{3-1}+6 \\ a_3=-3\times9+6 \\ a_3=-27+6 \\ a_3=-19 \end{gathered}$

for the fourth term,

put n = 4

$\begin{gathered} a_4=-3a_{4-1}+6 \\ a_4=-3a_3+6 \\ a_4=-3\times-19_{}+6 \\ a_4=57+6=63 \end{gathered}$

so the forth term is a4 = 63.