Question

Consider a sequence defined by the explicit rule f(n)=-8+3 (n - 1). Choose True or False for eachstatement.

Answer 1

Given the explicit rule for a determined arithmetic sequence:

`f(n)=-8+3(n-1)`

Where

a= -8 is the first term

d=3 is the common difference

and (n-1) represents any term of the sequence except the first one.

1) f(1)=-8

To prove if this statement is true or false, replace n=1 in the rule and calculate:

`\begin{gathered} f(1)=-8+3(1-1) \\ f(1)=-8+3\cdot0 \\ f(1)=-8 \end{gathered}`

As proved, the first term of the sequence is -8, the first statement is TRUE

2) The common difference is 3

For any explicit rule for an arithmetic sequence, the common difference is the coefficient that is mutliplied by (n-1), as mentioned above that is d=3

This statement is TRUE

3) The fifth term of the sequence is 7

To prove this statement you have to calculate the fifth term of the sequence, that is, replace the explicit rule with n=5:

`\begin{gathered} f(5)=-8+3(5-1) \\ f(5)=-8+3\cdot4 \\ f(5)=-8+12 \\ f(5)=4 \end{gathered}`

The fifth term of the sequence is 4, so this statement is FALSE