Question:
Find the missing term in the series:
\[
121,\;112,\;104,\;97,\;91,\;\_\_\_,\;82,\;79,\;77
\]
Find the missing term in the series:
\[
121,\;112,\;104,\;97,\;91,\;\_\_\_,\;82,\;79,\;77
\]
Show Hint
When differences form consecutive numbers in reverse order, continue the sequence carefully.
Updated On: Jul 15, 2026
- \(86\)
- \(85\)
- \(84\)
- \(83\)
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
Observe the pattern of subtraction.
The numbers decrease by consecutive integers.
Step 1: Find the differences.
\[ 121-112=9 \] \[ 112-104=8 \] \[ 104-97=7 \] \[ 97-91=6 \] Pattern: \[ -9,\;-8,\;-7,\;-6 \] So next should be: \[ -5,\;-4,\;-3,\;-2 \]
Step 2: Find the missing term.
After: \[ 91 \] subtract \(5\): \[ 91-5=86 \] Check further: \[ 86-4=82 \] \[ 82-3=79 \] \[ 79-2=77 \] Pattern matches perfectly. Thus, the missing term is: \[ \boxed{86} \]
Step 1: Find the differences.
\[ 121-112=9 \] \[ 112-104=8 \] \[ 104-97=7 \] \[ 97-91=6 \] Pattern: \[ -9,\;-8,\;-7,\;-6 \] So next should be: \[ -5,\;-4,\;-3,\;-2 \]
Step 2: Find the missing term.
After: \[ 91 \] subtract \(5\): \[ 91-5=86 \] Check further: \[ 86-4=82 \] \[ 82-3=79 \] \[ 79-2=77 \] Pattern matches perfectly. Thus, the missing term is: \[ \boxed{86} \]
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