Freeflows
Sequence Remainder Calculation 2
The infinite sequence $ T=\{t_0,t_1,t_2,\ldots\} $ is defined as $ t_0=0, $ $ t_1=1, $ and $ t_n=t_{n-2}+t_{n-1} $ for all integers $ n>1 .$ If $ a, $ $ b, $ $ c $ are fixed non-negative integers such that \begin{align*} a&\equiv 5\pmod {16}\\ b&\equiv 10\pmod {16}\\ c&\equiv 15\pmod {16}, \end{align*} then what is the remainder when $ t_a+t_b+t_c $ is divided by $ 7?$
- 1
- 2
- 3
- +
- 4
- 5
- 6
- -
- 7
- 8
- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$