Reviewed by Florence Khitsane
What is the next number? 1, 1, 2, 4, 3, 9, 4
Answer: The next number in the sequence 1, 1, 2, 4, 3, 9, 4 is 16
Number sequences often follow particular patterns or rules. Identifying the rule helps determine the next term. In this sequence, alternating between simple counting and squaring presents a pattern.
Methods
Math Tutor Explanation Using Alternating Patterns
This sequence uses two interwoven patterns: one increases by one, and the other squares each increase.
Step 1: Step 1: Separate the sequence into odd and even positions
Step 2: Step 2: Notice that numbers in odd positions increase by 1 (1, 2, 3, 4)
Math Tutor Explanation Using Formula Recognition
Observe a formula where a(n) is n/2 squared for even positions and (n+1)/2 for odd positions.
Step 1: Step 1: For odd indices (1, 3, 5, 7), the sequence is 1, 2, 3, 4 (i.e., (n+1)/2 for n=1,3,5,7)
Step 2: Step 2: For even indices (2, 4, 6, 8), the sequence is 1, 4, 9, ? (i.e., (n/2)^2 for n=2,4,6,8)
Step 1:
Step 2:
Math Tutor suggests: Practice Number Sequences and Patterns
Challenge yourself with more questions about number sequences, patterns, and what comes next in the series.
FAQ on Number Sequences
How do you spot patterns in a sequence?
Look for operations such as addition, multiplication, or alternating rules between terms.
What if a sequence alternates between two patterns?
Try splitting the sequence into two: one with odd positions, one with even, and analyze each separately.
Why do some sequences use squares?
Squaring is a common nonlinear pattern that creates rapidly increasing terms and is often inserted in sequences for complexity.
Can sequences have more than one rule?
Yes, some sequences alternate or layer multiple rules or operations for added complexity.
What does it mean if a pattern is not obvious?
It may involve more complex mathematics or an external context, and sometimes sequences have multiple plausible next terms.
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