Question

The zeros of $m\left(x\right)=\frac{x^2+3x+2}{x^2-3x+2}$ are the first two terms of a sequence. Each term in the sequence is found by adding the two terms before it. If each terms is smaller than the one before it, what is the fifth term of the sequence?

• A. $-8$
• B. $-5$
• C. $7$
• D. $8$
• E. $9$

Answer 1

Answer: (A)

$-8$

$x^2+3x+2=(x+1)(x+2)$ is $0$ at $x=-1,-2$
and it is given that'Each term in the sequence is found by adding the two terms before it'
so, the sequence should be like this $-1,-2,-3,-5,-8,-\mathrm{13................}$
As, we can see clearly that fifth term is $-8$
Therefore Answer is $A$