Answer:
-4
Step-by-step explanation:
The pattern or ratio in this geometric sequence is that you divide every term by -3/4. 27/16/-3/4=-9/4. Likewise, -9/4 divided by -3/4 equals 3. So then to find the next term in the sequence, just divide 3 by -3/4. When you do that, you get -4 as your answer.
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A geometric progression is a progression in which the ratio of any two consecutive terms is the same. The next term of the geometric sequence 27/16, -9/4, 3 is -4.
A geometric progression is a progression in which the ratio of any two consecutive terms is the same.
Suppose the initial term of a geometric sequence is a
and the term by which we multiply the previous term to get the next term is r.
Then the sequence would look like
a, ar, ar², ar³, .......
(till the terms to which it is defined)
Thus, the nth term of such sequence would be [tex]T_n = ar^{n-1}[/tex] (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
For the given geometric progression the common ratio is needed to be calculated in order to find the next term. Therefore, The common term of the given arithmetic progression is,
Common ratio, r = (27/16)/(-9/4)
= (27 × 4)/(16 × -9)
= -4/3
Now, the next term in a geometric progression is the product of the previous term and the common ratio. Therefore, the next term after 3 in the geometric progression is,
Next term = 3 × (-4 / 3) = -4
Hence, the next term of the geometric sequence 27/16, -9/4, 3 is -4.
Learn more about Geometric Sequence here:
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