Math CentralQuandaries & Queries


Question from Richard, a student:

Dear Sir/ madam,

This is my question about sequences.
Write down the nth term of the following sequences.

1/2, -3/4, 9/8, -27/16

Plz help me solve the question!
Thanks a lot!


Hi Richard,

In this sequence the numerators are powers of 3 (with alternating signs) and the denominators are powers of 2. Ignoring the alternating sign the numerators and denominators are

term number 1 2 3 4 ··· n
numerator 30 31 32 33 ···  
denominator 21 22 23 24 ···  

What values belong in the n column? To include the alternating sign multiply by (-1)n or (-1)n+1, whichever one works.

I hope this helps,

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