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

Question

2498 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-02T15:16:19

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

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 #n#th 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}}#

Answer 2 · 2018-07-02T15:21:18

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

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

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)#