Question

What is the formula for the nth term of the given sequence 100, 20, 4, …

Answer 1

`a_n=100 \left(\frac15\right)^(n-1)`

Explanation:

General equation of geometric sequence:
`a_n=ar^(n-1)`

Given:

• a₁ = 100
• a₂ = 20
• a₃ = 4

`\implies a_1=a=100`

`\implies a_2=100 \cdot r=20`

`\implies a_3=100 \cdot r^2=4`

Common ratio:

`r=(a_3)/(a_2)=(4)/(20)=\frac15`

Therefore:

`a_n=100 \left(\frac15\right)^(n-1)`