Write the five term sequence that would represent each recursive rule f(x) = f(x-1) -7; f(2) = 12

Required five terms of sequence are 19 , 12 , 5 , -2 and -9 .

Solution:

Need to find the five terms of the sequence.

Given recursive rule is f(x) = f(x-1) -7

Substituting x = 2 , f(2) = f(2-1)-7

= f(2) = f(1) – 7    (1)

Also given that f(2) = 12.  

On substituting the given value of f(2) in eq (1) we get

12 = f(1) – 7

f(1) = 12 + 7 = 19

Using given recursive rule and given value of f(2) calculating f(3)

Substituting x = 3 ,  

f(3) = f(3-1) – 7  

= f(2) – 7  

= 12 – 7  

= 5

Using given recursive rule and calculated  value of f(3) calculating f(4)

Substituting x = 4,  

f(4) = f(4-1) – 7  

= f(3) – 7  

= 5– 7  

= -2

Using given recursive rule and calculated  value of f(4) calculating f(5)

Substituting x = 5,  

f(5) = f(5-1) – 7  

= f(4) – 7  

= -2– 7  

= -9

Hence required five terms of sequence are 19 , 12 , 5 , -2 and -9 .

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