Question

The first term of a sequence is 2, the third term is 18, and the fifth term is 162. What is

Answer 1

Answer:

$a_2=6$

Step-by-step explanation:

Geometric sequence general formula:  $a_n=ar^{n-1}$

Given:

• $a_1=2$
• $a_3=18$
• $a_5=162$

Therefore,

$a_1=2 \implies a=2$

$a_3=2 \cdot r^2=18$

$a_5=2 \cdot r^4=162$

To find common ratio r, divide 5th and 3rd terms:

$\dfrac{a_5}{a_3}=\dfrac{2 \cdot r^4}{2 \cdot r^2}=\dfrac{162}{18}$

$\implies r^2=9$

$\implies r=\sqrt{9}=3$

Therefore, geometric sequence formula:  $a_n=2 \cdot 9^{n-1}$

So second term of sequence:

$\implies a_2=2 \cdot 3^{2-1}=6$