Question

Consider the sequence -8,-4, 0, 4, 8, 12,.... Select True or False for each statement

Answer 1

Try each statement to figure out if it holds or not.

`f(n)=-4(n-1)\text{ for all n}\ge2`

Try n=2, if the statement is true, then f(2) should be -4:

`f(2)=-4(2-1)=-4(1)=-4`

Try n=3, if the statement is true, then f(3) should be 0:

`f(3)=-4(3-1)=-4(2)=-8\text{ }!`

Therefore, the first statement is false.

Since the sequence is an arithmetic sequence, the first term is equal to -8 and the common difference of its terms is equal to 4, then the explicit rule for the sequence is:

`f(n)=-8+4(n-1)`

By trying different values of n you can convince yourself that this statement is true.

The tenth term is given by:

`\begin{gathered} f(10)=-8+4(10-1) \\ =-8+4(9) \\ =-8+36 \\ =28 \end{gathered}`

Therefore, the third statement is true.