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

Question

asked Nov 9, 2018 163k views

2 Answers

KristofferArl · Answer 1 · 2018-11-14T03:04:01+0000

It's geometric sequence:

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

Calculate the common ratio:

$r=(a_(n+1))/(a_n)\to r=(3)/(1.2)=2.5$

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"