Answer:
[tex]a_2=6[/tex]
Step-by-step explanation:
Geometric sequence general formula: [tex]a_n=ar^{n-1}[/tex]
Given:
Therefore,
[tex]a_1=2 \implies a=2[/tex]
[tex]a_3=2 \cdot r^2=18[/tex]
[tex]a_5=2 \cdot r^4=162[/tex]
To find common ratio r, divide 5th and 3rd terms:
[tex]\dfrac{a_5}{a_3}=\dfrac{2 \cdot r^4}{2 \cdot r^2}=\dfrac{162}{18}[/tex]
[tex]\implies r^2=9[/tex]
[tex]\implies r=\sqrt{9}=3[/tex]
Therefore, geometric sequence formula: [tex]a_n=2 \cdot 9^{n-1}[/tex]
So second term of sequence:
[tex]\implies a_2=2 \cdot 3^{2-1}=6[/tex]
