Question 1: Write the formula used to find the n-th term of a geometric sequence.

Answer: a_n = a_1 * r^(n-1)

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 16 and the common ratio is 2, what is the first term?

Answer: 2

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

Answer:

Question 5: A sequence starts with 5 and each term is multiplied by 4 to get the next. What is the 6th term?

Answer: 5120

Question 6: A toy company produces a model where the number of units sold each month forms a geometric sequence. If 100 units are sold in the first month and the ratio is 1.2, how many units are sold in the 4th month?

Answer: 207.36

Question 7: Identify the common mistake in applying the formula: "a_n = a_1 * r^(n+1)" for the n-th term of a geometric sequence.

Answer: Using n+1 instead of n-1 in the exponent

Question 8: Given a sequence where a_1 = 2 and a_4 = 16, find the common ratio.

Answer: 2

Question 9: Construct a geometric sequence with a first term of 7 and a common ratio of 0.5. Write the first four terms.

Answer:

Question 10: A student mistakenly applies the formula with r = 1.5 when the actual ratio is 0.75. How does this error affect the calculation of the 5th term if the first term is 10?

Answer: It overestimates the 5th term, giving a much larger value than correct.

Question 11: Find the 8th term of a geometric sequence where a_1 = 4 and r = 0.5.

Answer: 0.5