Answer:
y=-6
Step-by-step explanation:
Geometric Sequences
Any given sequence is said to be geometric if each term [tex]a_n[/tex] can be obtained as the previous term [tex]a_{n-1}[/tex] by a constant value called the common ratio.
[tex]a_n=a_{n-1}.r[/tex]
or equivalently
[tex]a_n=a_1.r^{n-1}[/tex]
Looking closely at the sequence 2, y, 18,-54, 162 we can try to find out if it's a geometric sequence or not. We compute the possible common ratios
[tex]\displaystyle \frac{162}{-54},\ \frac{-54}{18}[/tex] and we see they both result -3. If we use r=-3 and try to find the second term (y), then
y=2*(-3)=-6
Now we compute the third term: (-6)(-3)=18
Since we got the third term as given in the original sequence.
So y=-6
