Question 1: What is the next number in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ?

Answer: 13

Question 2: Calculate the 7th term of the sequence where each term after the first two is obtained by adding the previous two terms: 2, 3, ?, ?, ?

Answer: 8, 11, 19

Question 3: In a star cluster, the number of stars in each successive spiral pattern doubles. If the first pattern has 50 stars, how many stars are in the 4th pattern?

Answer: 400

Question 4: Identify the pattern: 3, 6, 12, 24, ?

Answer: 48

Question 5: A telescope observes a sequence of planets where the distance from the Sun doubles each time: 50 million km, 100 million km, 200 million km. What is the distance to the fifth planet?

Answer: 400 million km

Question 6: Construct a sequence where each term is three times the previous term, starting with 2. List the first four terms.

Answer: 2, 6, 18, 54

Question 7: A spacecraft's fuel consumption increases according to the Fibonacci sequence after each orbit: 1, 1, 2, 3, 5. How much fuel will it consume after the 6th orbit?

Answer: 8

Question 8: Explain why the sequence 2, 4, 8, 16, ? is a geometric sequence. What is the common ratio?

Answer: Each term is multiplied by 2, so the common ratio is 2.

Question 9: A pattern of star brightness levels follows a sequence: 1, 4, 9, 16, ?. What is the next brightness level?

Answer: 25

Question 10: Identify the mistake in this sequence: 2, 4, 8, 15, 16. What should the correct sequence be if it is based on doubling?

Answer: The sequence should be 2, 4, 8, 16, 32.

Question 11: Challenge: Find the 10th term of a sequence where each term increases by adding the previous two terms, starting with 1 and 1.

Answer: 144