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SAT Math Practice Question #25871 - SATify | SATify

#25871

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 $(a_{n + 1}, b_{n + 1}) = (a_{n} + b_{n}, - a_{n} + b_{n})$ for $n = 1, 2, 3, \dots$ . Suppose that $(a_{60}, b_{60}) = (0, 16)$ . What is $a_{1} + b_{1}$ ?

A.

$- 2^{- 27}$

B.

$- 2^{- 26}$

C.

$- 2^{- 25}$

D.

$2^{- 26}$

E.

$2^{- 25}$