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

Mathematics

1 answer:

Naily [24]1 year ago

6 0

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:

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

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navik [9.2K]

Hello.

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