Question

What is the next term of the geometric sequence? 27 16 , − 9 4 , 3 , 16 27 ​ ,− 4 9 ​ ,3,start fraction, 27, divided by, 16, end fraction, comma, minus, start fraction, 9, divided by, 4, end fraction, comma, 3, comma

Answer 1

The next term of the geometric sequence is 1/48.

Step-by-step explanation:

The given sequence is 27, 16, -9/4, 3, 16/27, -4/9, 3. This appears to be a sequence in which the denominator of each term is the numerator of the next term, and the numerator of each term is the numerator of the previous term times -1 raised to the power of the term number.

Using this pattern, the next term would have a numerator of -1 raised to the power of 8 (-1^8 = 1), and a denominator of 3 times the numerator of the previous term (3 * 16 = 48).

Therefore, the next term of the sequence is 1/48.