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,…

Question

asked Jun 16, 2018 110k views

2 Answers

Wmac · Answer 1 · 2018-06-18T13:09:36+0000

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

Vikko · Answer 2 · 2018-06-20T21:42:06+0000

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.