Question

Please help me

What are the first four terms of the sequence defined recursively below?
a1=5
an=(-1)^n+3an-1+2

A. 5, 16, 51, 154
B. 5, 18, 16, 18
C. 5, 16, 49, 148
D. 5, 18, 55, 168

Answer 1

Your answer is D. plug 18 into the equation and you'll get 55. if you try to plug in any other number from A,B,OR C, you will not get the answer

Answer 2

Answer: Option 'D' is correct.

Explanation:

Since we have given that

`a_1=5`

and

`a_n=(-1)^n+3a_(n-1)+2\\`

We have to find the first four terms of the sequence :

For n = 2,

`a_2=(-1)^2+3a_(2-1)+2\\\\a_2=1+3a_1+2\\\\a_2=1+3* 5+2\\\\a_2=1+15+2=18`

For n = 3,

`a_3=(-1)^3+3a_(3-1)+2\\\\a_3=-1+3a_2+2\\\\a_3=-1+3* 18+2\\\\a_2=-1+54+2=55`

For n = 4,

`a_4=(-1)^4+3a_(4-1)+2\\\\a_4=1+3a_3+2\\\\a_4=1+3* 55+2\\\\a_2=1+165+2=168`

So, the first four terms of the sequence is given by

`5,18,55,168`

Hence, Option 'D' is correct.