Every geometric sequence can be described by a function known as the explicit rule which receives as input the position of a term n, and returns as output the term's value The explicit rule for a geometric sequence has the following general form.
|n||Using a1 and r|
Pelle's good friend, Lisa, decides to play a trick on Pelle. While he is away, she rearranges his pellets so that they are grouped in a geometric sequence instead of an arithmetic one. The first group has 2 pellets, the second has 6, the third has 18, and so on. Find a rule describing this sequence. After finishing the seventh group, Lisa counted 3273 remaining pellets. Use the rule to figure out whether there are enough to make an eighth group.
The terms we've been given are not consecutive. Therefore, we can't directly find r. However, the terms a2 and a4 are 2 positions apart, so the ratio between them must be r2.
The desired explicit rule is We already know the terms a1,a2, and a4. Let's use the rule to find the remaining three.
The terms a5 and a6 are evaluated similarly.