How to find a geometric rule for a recursive sequence

The video tutorial explains how to determine the first five terms of a sequence using a geometric rule. It starts with calculating the terms by following a pattern and then discusses how to identify the rule governing the sequence. The tutorial emphasizes the geometric rule, A of N equals A of 1 times R raised to the N minus 1, and demonstrates its application. The video also contrasts arithmetic and geometric sequences, highlighting the importance of understanding the difference for test preparation.

What is the value of the third term in the sequence if the first term is 5 and the rule is to multiply the previous term by -2?

• 10

• -10

• -20

• 20

Which of the following statements is true about arithmetic sequences?

• The difference between consecutive terms is constant.

• The ratio between consecutive terms is constant.

• The terms are always negative.

• The terms are always positive.

In a geometric sequence, if the first term is 5 and the common ratio is -2, what is the formula for the nth term?

• A(n) = 5 + (-2)^(n-1)

• A(n) = 5 * 2^(n-1)

• A(n) = 5 - 2^(n-1)

• A(n) = 5 * (-2)^(n-1)

How can you determine if a sequence is geometric?

• By checking if the ratio between terms is constant.

• By checking if the difference between terms is constant.

• By checking if the product of terms is constant.

• By checking if the sum of terms is constant.

What is the common ratio in a sequence where the first term is 5 and the second term is -10?

• -1

• 2

• -2

• 1