Question

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

the second term of the sequence?

Answer 1

`a_2=6`

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:

`(a_5)/(a_3)=(2 \cdot r^4)/(2 \cdot r^2)=(162)/(18)`

`\implies r^2=9`

`\implies r=√(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`