Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex]a_1=5[/tex]
and
[tex]a_n=(-1)^n+3a_{n-1}+2\\[/tex]
We have to find the first four terms of the sequence :
For n = 2,
[tex]a_2=(-1)^2+3a_{2-1}+2\\\\a_2=1+3a_1+2\\\\a_2=1+3\times 5+2\\\\a_2=1+15+2=18[/tex]
For n = 3,
[tex]a_3=(-1)^3+3a_{3-1}+2\\\\a_3=-1+3a_2+2\\\\a_3=-1+3\times 18+2\\\\a_2=-1+54+2=55[/tex]
For n = 4,
[tex]a_4=(-1)^4+3a_{4-1}+2\\\\a_4=1+3a_3+2\\\\a_4=1+3\times 55+2\\\\a_2=1+165+2=168[/tex]
So, the first four terms of the sequence is given by
[tex]5,18,55,168[/tex]
Hence, Option 'D' is correct.
