Question 1: Write the formula for the nth term of a geometric sequence and explain each component.

Answer: The nth term an = a1 * r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number.

Question 2: Calculate the 5th term of a geometric sequence where the first term is 3 and the common ratio is 2.

Answer: 48

Question 3: If the 3rd term of a geometric sequence is 24 and the common ratio is 2, find the first term, a1.

Answer: a1=6

Question 4: Plot the graph of y = 2 * 3^(x-1) for x = 1 to 5 on the grid.

Answer: Points: (1,2), (2,6), (3,18), (4,54), (5,162)

Question 5: Construct a geometric sequence with first term 5 and common ratio 0.5. Find the first four terms.

Answer: [5, 2.5, 1.25, 0.625]

Question 6: A ball is dropped from a height of 100 meters and bounces back to 60% of its previous height each time. Find the height after the 4th bounce.

Answer: Approximately 12.96 meters

Question 7: Given a geometric sequence where a1 = 8 and the 6th term is 128, find the common ratio r.

Answer: r=2

Question 8: Identify the error in this statement: 'If the first term is 4 and the ratio is 3, then the third term is 36.'

Answer: Incorrect, the third term is 4 * 3^(3-1) = 4 * 3^2 = 36, so the statement is actually correct. Provide an example of a common mistake.

Question 9: Calculate the sum of the first 5 terms of a geometric sequence where a1 = 2 and r = 3.

Answer: S5= 2*(3^5 - 1)/(3 - 1) = 2*(243-1)/2= 242

Question 10: A sequence is defined by the formula an = 7 * (0.5)^(n-1). What is the 10th term?

Answer: 0.35

Question 11: Determine whether the sequence with first term 10 and ratio 1 equals a geometric sequence. Justify your answer.

Answer: Yes, because each term is obtained by multiplying the previous term by 1, maintaining constant ratio.

Question 12: Challenge: Find the first term of a geometric sequence if the 8th term is 512 and the ratio is 2.

Answer: a1=1