Recursive and Explicit Rules for Geometric Sequences

The video tutorial explains geometric sequences, focusing on both explicit and recursive rules. It begins with an introduction to geometric sequences and the explicit rule, followed by deriving the explicit rule for a sequence and calculating specific terms. The tutorial then shifts to recursive sequences, highlighting common mistakes and comparing both rules through examples. The video concludes by reinforcing that both rules yield the same results when applied correctly.

What is the explicit formula for finding the nth term in a geometric sequence?

• a sub n equals a sub 1 divided by r to the n minus 1 power

• a sub n equals a sub 1 minus r to the n minus 1 power

• a sub n equals a sub 1 times r to the n minus 1 power

• a sub n equals a sub 1 plus r to the n minus 1 power

In a geometric sequence, how is each term related to the previous term?

• Each term is subtracted from the previous term

• Each term is multiplied by a common ratio

• Each term is divided by the previous term

• Each term is added to the previous term

What is a common mistake when using the recursive rule for geometric sequences?

• Confusing the common ratio with the first term

• Using addition instead of multiplication

• Using division instead of multiplication

• Forgetting to subtract one from n

What is the recursive formula for a geometric sequence?

• a sub n equals a sub 1 times a sub n minus 1

• a sub n equals a sub 1 divided by a sub n minus 1

• a sub n equals a sub 1 plus a sub n minus 1

• a sub n equals r times a sub n minus 1

How do the explicit and recursive rules compare when finding terms in a geometric sequence?

• They give the same result only for even terms

• They give the same result for any term in the sequence

• They give the same result for the first term only

• They always give different results

What is the fifth term in a sequence with a first term of 4 and a common ratio of 3 using the explicit rule?

• 81

• 243

• 108

• 324

Using the recursive rule, what is the fifth term in a sequence where the fourth term is 108 and the common ratio is 3?

• 216

• 108

• 432

• 324