155k views
5 votes
Consider the sequence -8,-4, 0, 4, 8, 12,.... Select True or False for each statement

Consider the sequence -8,-4, 0, 4, 8, 12,.... Select True or False for each statement-example-1

1 Answer

3 votes

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.

User Aki
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories