Question

The first term in sequence A is 6 and the third is 72. Which of the following equations could define sequence A for all positive values of n?

1) 3(An-1)+2n
2) 12(An-1)
3) 6(An-1)+18n
4) 6(An-1)-6
5) 3(An-1)+2

Answer 1

The correct equation to define sequence A where the first term is 6 and the third term is 72 is An = 12(An-1), meaning each term is 12 times the previous term. This makes option 2 the right choice.

Step-by-step explanation:

The student's question asks for the correct equation that could define sequence A given the first and third terms of the sequence. To find the correct equation, we need to examine how the sequence progresses from the first term (6) to the third term (72), and identify the rule that makes this progression possible.

Before checking the provided options, we have the following information:

The first term, A1, is 6.

The third term, A3, is 72.

The general form for a recursive sequence is An = f(An-1), where f is some function of the previous term. Considering the options given, we need an equation such that applying it twice (from A1 to A2, and from A2 to A3) results in the third term being 72.

Option 2) 12(An-1) suggests a sequence where each term is 12 times the previous term. This fits with our sequence as 6 * 12 = 72. Thus, for the student's sequence, An = 12(An-1) is the correct formula that defines sequence A for all positive values of n, making option 2 the correct answer.