Introduction to the function

Question

The nth term of a sequence is given by the function T=52-6n.

(a)write down the first three terms of the sequence.

(b)Find the domain of the function.

(c)Mark claims that 8 is a term in the sequence. Do you agree? Explain your answer.

Answer 1

For n=1, T = 52 - 6(1) = 52 - 6 = 46

n=2 , T = 52 - 6(2) = 52 - 12 = 40

n=3, T = 52 - 6(3) = 52 - 18 = 34

THe domain is the set of positive integers n=1,2,3,4,....

If 8 is a term in this sequence, then 8 = 52 - 6n for some positive integer n.

-44 = -6n <--- subtracts 52 from both sides

44/6 = n <-- divides both sides by -6

22/3 = n

Since 22/3 is not a positive integer, then 8 is not a term in the sequence and Mark is incorrect.

For n = 6, 52 - 6(6) = 52 - 36 = 16

n=7, 52 - 6(7) = 52 - 42 = 10

n=8 , 52 - 6(8) = 52 - 48 = 4