turkey-yks 2010 Q31

turkey-yks · Other · lys1-math Arithmetic Sequences and Series Sequence Defined by Recurrence with AP Connection

The sequences $\{a_{n}\}$ and $\{b_{n}\}$ are defined as follows. $$a_{n} = \begin{cases} 0, & \text{if } n \equiv 0 \pmod{3} \\ n, & \text{if } n \equiv 1 \pmod{3} \\ -n, & \text{if } n \equiv 2 \pmod{3} \end{cases}, \quad b_{n} = \sum_{k=0}^{n} a_{k}$$ Accordingly, what is $b_{4}$?
A) $-2$
B) $-1$
C) $0$
D) $2$
E) $3$

The sequences $\{a_{n}\}$ and $\{b_{n}\}$ are defined as follows.
$$a_{n} = \begin{cases} 0, & \text{if } n \equiv 0 \pmod{3} \\ n, & \text{if } n \equiv 1 \pmod{3} \\ -n, & \text{if } n \equiv 2 \pmod{3} \end{cases}, \quad b_{n} = \sum_{k=0}^{n} a_{k}$$
Accordingly, what is $b_{4}$?

A) $-2$\\
B) $-1$\\
C) $0$\\
D) $2$\\
E) $3$

Paper Questions

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