Question 1: Calculate the 5th term of a geometric sequence where the first term is 3 and the common ratio is 2.

Answer: 48

Question 2: If the 1st term of a sequence is 5 and the 4th term is 40, find the common ratio.

Answer: 2

Question 3: Write the general formula for the nth term of a geometric sequence where the first term is a₁ and the common ratio is r.

Answer: aₙ= a₁×r⁽ⁿ⁻¹⁾

Question 4: Calculate the 7th term of a sequence with a₁=4 and r=3.

Answer: 729

Question 5: A bacteria population starts with 200 bacteria and doubles every hour. How many bacteria are there after 6 hours?

Answer: 12800

Question 6: The value of an investment grows by 10% each year. If the initial amount is $1000, what will be its value after 3 years?

Answer: $1331

Question 7: A staircase has 15 steps. The number of tiles used on each step forms a geometric sequence starting with 2 tiles on the first step and increasing by a ratio of 1.5. How many tiles are used on the 10th step?

Answer: 38

Question 8: Given the sequence: 5, 10, 20, 40, ... which term is equal to 160?

Answer: 5th

Question 9: A radioactive substance decays so that its amount every day is half of what it was the previous day. If you start with 100 grams, how much remains after 4 days?

Answer: 6.25

Question 10: Identify and correct the mistake in this statement: 'In a geometric sequence, the common ratio is obtained by dividing any term by the previous term.'

Answer: No mistake; statement is correct.

Question 11: Challenge: The first term of a sequence is 2. The 8th term is 128. Find the common ratio and write the formula for the nth term.

Answer: r=2, aₙ= 2×2⁽ⁿ⁻¹⁾