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SAT Math Practice Question #25870 - SATify | SATify

#25870

sequences and series

algebra

Relative Motion

hard

120 sec

A sequence $(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3}), \dots$ of points in the coordinate plane satisfies $(a_{n + 1}, b_{n + 1}) = (a_{n} + 3 b_{n}, - 3 a_{n} + b_{n})$ for $n = 1, 2, 3, \dots$ . Suppose that $(a_{70}, b_{70}) = (6, 2)$ . What is $a_{1} - b_{1}$ ?

A.

$- 2^{- 66}$

B.

$- 2^{- 67}$

C.

$0$

D.

$2^{- 67}$

E.

$2^{- 66}$