Think logically not mathematically [part-31]

an=15[(1+52)n(152)n]a_{n} = \frac{1}{\sqrt{5}}\left[ \left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{1-\sqrt{5}}{2}\right)^n\right] Consider a sequence of real numbers {an}\{a_n\} as given above, where nn is a non-negative integer. Then which of the following are correct? \[\begin{array} {} \text{A)} & a_{5} & = & 5 \\ \text{B)} & a_{12} & = & 12^2 \\ \text{C)} & a_{10} & = & 55 \\ \text{D)} & a_{2009} + a_{2010} & = & 2 \ a_{2011} \end{array} \]

×

Problem Loading...

Note Loading...

Set Loading...