This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey, good to see you again. Step 1: Analyze the given pattern. The given pattern is 6, 3, 12, 5, 24, 7, 48, 9, Observe the terms at odd positions (1^st, 3^rd, 5^th, 7^th): 6, 12, 24, 48. Observe the terms at even positions (2^nd, 4^th, 6^th, 8^th): 3, 5, 7, 9. Step 2: Identify the rule for each interleaved sequence. For the terms at odd positions (6, 12, 24, 48): Each term is obtained by multiplying the previous term in this sequence by 2. 6 × 2 = 12 12 × 2 = 24 24 × 2 = 48 For the terms at even positions (3, 5, 7, 9): Each term is obtained by adding 2 to the previous term in this sequence. 3 + 2 = 5 5 + 2 = 7 7 + 2 = 9 Step 3: Extend the pattern by the next three terms. The last given term is 9, which is the 8^th term (an even position). The 9^th term will follow the rule for odd positions: 9^th term = 48 × 2 = 96. The 10^th term will follow the rule for even positions: 10^th term = 9 + 2 = 11. The 11^th term will follow the rule for odd positions: 11^th term = 96 × 2 = 192. The next three terms are 96, 11, 192. Explanation: The pattern consists of two interleaved sequences. The terms at odd positions (1^st, 3^rd, 5^th, ) form a geometric progression where each term is multiplied by 2. The terms at even positions (2^nd, 4^th, 6^th, ) form an arithmetic progression where 2 is added to each term. The extended pattern is: 6, 3, 12, 5, 24, 7, 48, 9, 96, 11, 192. Send me the next one 📸