Understanding Geometric Sequences

The video tutorial explains how to determine the first five terms of a geometric sequence with a given first term and common ratio. It demonstrates two methods: using a formula and an iterative approach. The formula method involves substituting values into the formula A sub N equals A sub one times R to the power of N minus one. The iterative method involves multiplying the previous term by the common ratio. Both methods yield the same results, confirming their validity. The tutorial concludes by summarizing the process and results.

What is the first term of the sequence given in the problem?

• 16

• 2

• 4

• 8

What is the common ratio of the sequence?

• 1/4

• 1/2

• 1/5

• 1/3

Which formula is used to find the nth term of a geometric sequence?

• A sub N equals A sub one divided by R to the power of N

• A sub N equals A sub one minus R times N

• A sub N equals A sub one times R to the power of N minus one

• A sub N equals A sub one plus R times N

What is the second term of the sequence using the recursive formula?

• 2

• 6

• 4

• 8

How is the third term calculated using the recursive formula?

• Multiply the first term by the common ratio

• Multiply the second term by the common ratio

• Add the common ratio to the second term

• Subtract the common ratio from the second term

What is the fourth term of the sequence?

• 1/2

• 1/16

• 1/4

• 1/8

What is the fifth term of the sequence using the recursive formula?

• 1/64

• 1/16

• 1/128

• 1/32

How does the alternative formula verify the second term?

• By subtracting the common ratio from the first term

• By adding the common ratio to the first term

• By multiplying the first term by the common ratio

• By dividing the first term by the common ratio

What is the result of using the alternative formula for the fifth term?

• 1/16

• 1/32

• 1/64

• 1/128

What conclusion is drawn about the two methods used?

• They are not applicable

• They yield the same results

• They are both incorrect

• They give different results