In the Trivia Bowl, each finalist must answer four questions correctly. Each question is worth twice as much as the question before it. The fourth question is worth $6000. How much is the first question worth?

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Answer 1 · 2016-07-19T23:34:21

This is a geometric sequence, where #r = 2#, #n = 4#, and #t_4 = 6000#. We will be solving for #a#.

#t_n = a xx r^(n - 1)#

#6000 = a xx 2^(4 - 1)#

#6000 = a xx 2^3#

#6000 = 8a#

#a = 750#

Hence, the first question is worth 750 marks.

Hopefully this helps!