1.2, 3, 7.5, 18.75, ... which formula can be used to describe the sequence?

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 360 People

1.2, 3, 7.5, 18.75, ...
Which formula can be used to describe the sequence?

f(x) = 1.2(2.5)x – 1
f(x) = 2.5(1.2)x – 1
f(x) = 1.2(2.5)x
f(x) = 2.5(1.2)x

Answered by maham237 @ 26/12/2020

It's geometric sequence:

$a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....$

Calculate the common ratio:

$r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5$

The explicit formula of geometric sequence:

$a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}$

Substitute:

$a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}$

Answer: "f(x) = 1.2(2.5)x-1"

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