Math Is Fun Forum

lisathedork

Member

Registered: 2013-10-24

Posts: 36

Recursion and Special Sequences

Hello, I need help with the following problems. I don't understand the information that my textbook provides.

1. Find the 4th term if the sequence in which a1 = 2 and a(n+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 refrigerator in three years if the rate of inflation remains consistant.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Recursion and Special Sequences

hi Lisa,

These are examples of 'iterative' formulas.  That means that the value of the next term is governed by the previous term and some formula.  In Q1 the bits after the a are subscripts thus:

Turning that into English this means that the first term is 2 and subsequent terms are calculated by multiplying a term by -4 and adding 2 to get the next term.

So

and

I'll leave you do complete the calculations.

Q2.  Same idea :

Keep going until you have calculated

Q3.  Each year the cost goes up by multiplying the previous cost by 1.03 so do this three times.

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob