Question

A sequence is defined by

Answer 1

I believe the answer is D.

3^2 is 9 and 4^2 is 16, and because 9/16 was the third term in the sequence, you raise both the numerator and the denominator by the number of the term minus 1.

So to find the seventh term, you raise the numerator and denominator by 7 - 1 = 6.

So the answer is 729/4096

Answer 2

Since each term is -3/4 times the previous term we know that this is a geometric sequence with a common ratio of -3/4.  Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number

Since we do know the common ratio is -3/4 and that a(3)=9/16 we can find the value of a, the initial term.

9/16=a(-3/4)^2

9/16=9a/16

1=a, so the initial term is 1 so now we have the formula for our geometric sequence.

a(n)=1*(-3/4)^(n-1)

a(n)=(-3/4)^(n-1)  so the 7th term is:

a(7)=(-3/4)^6

a(7)=729/4096