Question

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

Answer 1

Answer:

$a_n=100 \left(\dfrac15\right)^{n-1}$

Step-by-step 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:

$r=\dfrac{a_3}{a_2}=\dfrac{4}{20}=\dfrac15$

Therefore:

$a_n=100 \left(\dfrac15\right)^{n-1}$