Study the number sequence below.<br><br>3, 7, 5, 13, 7, 19, 9, 25, ___<br><br>What is the next term in the sequence?
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Worked Solution
Step 1: Separate the sequence into two interleaved sub-sequences by position.
Odd positions (1st, 3rd, 5th, 7th, 9th): 3, 5, 7, 9, ___
Even positions (2nd, 4th, 6th, 8th): 7, 13, 19, 25
Step 2: Find the rule for each sub-sequence.
Odd-position sub-sequence: 3, 5, 7, 9 — common difference = 2.
Even-position sub-sequence: 7, 13, 19, 25 — common difference = 6.
Step 3: Identify the position of the blank. The sequence has 8 terms shown, so the blank is the 9th term. Position 9 is odd.
Step 4: Apply the odd-position rule. The 4th odd-position term is 9; the 5th is 9 + 2 = 11.
Answer: 11
Correct answer: 11
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