JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q63

← JEE Main 2015 · 4 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 63 of 90

Let α and β be the roots of equation $x^2-6x-2=0$ . If $a_n=\alpha^n-\beta^n$ , for $n\ge1$ , then the value of $\dfrac{a_{10}-2a_8}{2a_9}$ is equal to :

−6

−3

Answer and worked solution

Official answer: C

α and β satisfy $t^2=6t+2$ , so $a_{n+2}=6a_{n+1}+2a_n$ . Then $a_{10}-2a_8=6a_9$ , and
$\frac{a_{10}-2a_8}{2a_9}=3.$

Topics:Roots and coefficients Special series sums

← Previous question Next question →

JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 63