write a recursive rule for the sequence -5,10,-20,40,-80,...

Question

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Answer 1

The common ratio is -2.

 

A recursive definition usually defines a₁ (the base case) and any other constant terms, then defines a_n in terms of a_n-1 or other already defined terms (recursive case).  This is so recursion is done to produce a_n.

 

a₁ = -5                [base case]

a_n = -2a_n-1           [recursive case]

Answer 2

a_n+1 = -2a_n

Answer 3

The common ratio is -2.

 

-5 * -2 = 10

 

10 * -2 = -20

 

-20 * -2 = 40

 

Based on this pattern, you are taking the previous value and multiplying it by -2.

 

f(1) = -5

 

Then the formula is

 

f(n + 1) = -2f(n)

 

where:  

n is the nth sequence

f(n) is the previous term

f(n + 1) is the new term