Question:
Find the missing term in the series:
\[ 1,\ 2,\ 6,\ 15,\ 31,\ 56,\ \underline{\hspace{1cm}} \]
Find the missing term in the series:
\[ 1,\ 2,\ 6,\ 15,\ 31,\ 56,\ \underline{\hspace{1cm}} \]
Show Hint
Whenever the terms do not reveal an obvious pattern, calculate first differences. Perfect squares, cubes, and prime numbers frequently appear in difference sequences.
Updated On: Jun 13, 2026
- 88
- 92
- 94
- 96
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
Many numerical series are generated by adding terms that themselves follow a recognizable pattern. Therefore, before looking at the terms directly, it is often useful to examine the first differences.
Step 1: Find the successive differences. \[ 2-1=1 \] \[ 6-2=4 \] \[ 15-6=9 \] \[ 31-15=16 \] \[ 56-31=25 \] Thus the sequence of differences is \[ 1,\ 4,\ 9,\ 16,\ 25. \]
Step 2: Recognize the pattern. These are perfect squares: \[ 1^2,\ 2^2,\ 3^2,\ 4^2,\ 5^2. \] Hence the next difference should be \[ 6^2=36. \]
Step 3: Find the next term. Adding the next difference: \[ 56+36=92. \] Therefore the missing term is \[ \boxed{92}. \]
Step 1: Find the successive differences. \[ 2-1=1 \] \[ 6-2=4 \] \[ 15-6=9 \] \[ 31-15=16 \] \[ 56-31=25 \] Thus the sequence of differences is \[ 1,\ 4,\ 9,\ 16,\ 25. \]
Step 2: Recognize the pattern. These are perfect squares: \[ 1^2,\ 2^2,\ 3^2,\ 4^2,\ 5^2. \] Hence the next difference should be \[ 6^2=36. \]
Step 3: Find the next term. Adding the next difference: \[ 56+36=92. \] Therefore the missing term is \[ \boxed{92}. \]
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