What would the formula for the nth term be given 0.3, -0.06, 0.012, -0.0024, 0.00048, ...?

2 Answers

a_n=\frac{0.3}{(-5)^{n-1}}

Explanation:

Given series: 0.3, -0.06, 0.012, -0.0024, 0.00048\ldots

has first term a=0.3 & a common ratio r is given as follows

r=\frac{-0.06}{0.3}=\frac{0.012}{-0.06}=\ldots=-1/5

Now, the nth term of above Geometric progression (GP) will be as follows

a_n=ar^{n-1}

a_n=0.3(-1/5)^{n-1}

a_n=\frac{0.3}{(-5)^{n-1}}

Jul 2, 2018

=>n^(th)term of the sequence is :

a_n=(0.3)(-0.2)^(n-1)

Explanation:

Here, the given sequence is :

0.3,-0.06,0.012,-0.0024,0.00048,...

The first term =a_1=0.3

The common ratio :

r=(-0.06)/0.3=(0.012)/(-0.06)=(-0.0024)/0.012=(0.00048)/(-0.0024)=-0.2

This is the geometric sequence :

=>n^(th)term of the sequence is :

a_n=a_1(r)^(n-1)

=>a_n=(0.3)(-0.2)^(n-1)