Question

1) Find the 4th term if the sequend in which a1 = 2 and an+1 = -4an + 2.

2) Find the third iterate, x3, of the function f(x) = 3x + 5 for an initial value of x0 = 1.

3)The rate of inflation is 3%. The cost of an item in future years can be found by iterating the function c(x) = 1.03x. Find the cost of a $1500 refigerator in three years if the rate of inflation remains consistant.
a. $1539.99
b. $1639.09
c. $1545.00

PLEASE HELP !

Answer 1

A1 = 2
An+1 = - 4 An + 2
For the 4th term, put n = 3

It is easier to find A2, then A3 and then A4
A2 = - 4 A1 + 2 = -4 * 2 +2 = -6
A3 = - 4 A2 + 2 = 24 + 2 = 26
A4 = - 4 * 26 + 2 = -102
================================

3) cost after one year = 1.03 * $1500
cost after two years = 1.03 (1.03 * $1500)
cost after 3 years = 1.03 * [ 1.03 * (1.03 * $1500) ] = 1.03³ * $1500
= $ 1639.09