What is the explicit rule for this geometric sequence?

4, 4/5, 4/25, 4/125,…

What is the recursive rule for this geometric sequence?

1/2, −2, 8, −32,...

What is the explicit rule for this geometric sequence?

a_{1}=2/3;a_{n}=9⋅a_{n}−1

A business owes $8000 on a loan. Every month, the business pays 1/2 of the amount remaining on the loan.

How much will the business pay in the sixth month?

Guest Dec 6, 2017

#1**+1 **

4, 4/5, 4/25, 4/125 ..... = 4(1/5)^(n - 1) where n is the nth term

1/2, -2, 8 , - 32......

a_{1} = (1/2) , a_{n} = (-4) *a_{n-1}

a_{1}=2/3;a_{n}=9⋅a_{n−1}

The terms are 2/3, 6, 54, 486......so the explicit formula is

(2/3)*9^(n - 1) where n is the nth term

8000*(1/2)^6.......in the 6th month, the business pays $125

CPhill
Dec 7, 2017