ShmoopTube

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And here's your shmoop du jour...

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Each term in a sequence is one less than twice the previous term.

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If the 5th term is 33, what is the first term?

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Here are the potential answers...

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So what do we know so far?

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We know that in the sequence, the 5th term, n sub 5, is equal to 33,

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and each subsequent term is one less than twice the previous...

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...2 times the previous minus 1... is the equation.

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However, we want to solve for the first term,

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so instead of finding the next term, we want to go backwards.

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We can solve the equation for n sub a, and then we'll be able to do that.

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We add 1 to both sides, and then divide by 2.

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We get that n sub a is equal to n sub a plus 1 plus 1 over 2.

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So now, if we set n sub a plus 1 equal to 33, we can find the previous term, the fourth.

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33 + 1 is 34; divide by 2 and we get 17.

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So let's plug in 17 back into the equation, we get 17 + 1 = 18, over 2 which is 9.

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This time, we plug in...9 + 1 which is 10, over 2 is 5.

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Last one. 5 plus 1 is 6, over 2 is 3.

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Finally, we get our answer.

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The first term in our sequence is 3, so our answer is (B).

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