Question:
Find the missing term in the series:
\[
99,\;98,\;94,\;85,\;69,\;\_\_\_,\;8,\;-41,\;-105
\]
Find the missing term in the series:
\[
99,\;98,\;94,\;85,\;69,\;\_\_\_,\;8,\;-41,\;-105
\]
Show Hint
When differences form perfect squares, cubes, or consecutive patterns, it becomes easier to predict missing terms.
Updated On: Jul 15, 2026
- \(48\)
- \(44\)
- \(36\)
- \(19\)
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
Observe the differences between consecutive terms.
Step 1: Find the differences.
\[ 98-99=-1 \] \[ 94-98=-4 \] \[ 85-94=-9 \] \[ 69-85=-16 \] These are: \[ -1^2,\;-2^2,\;-3^2,\;-4^2 \]
Step 2: Continue the pattern.
Next differences should be: \[ -5^2,\;-6^2,\;-7^2,\;-8^2 \] That is: \[ -25,\;-36,\;-49,\;-64 \]
Step 3: Find the missing term.
From: \[ 69-25=44 \] Check further: \[ 44-36=8 \] \[ 8-49=-41 \] \[ -41-64=-105 \] Pattern matches perfectly. Thus, the missing term is: \[ \boxed{44} \]
Step 1: Find the differences.
\[ 98-99=-1 \] \[ 94-98=-4 \] \[ 85-94=-9 \] \[ 69-85=-16 \] These are: \[ -1^2,\;-2^2,\;-3^2,\;-4^2 \]
Step 2: Continue the pattern.
Next differences should be: \[ -5^2,\;-6^2,\;-7^2,\;-8^2 \] That is: \[ -25,\;-36,\;-49,\;-64 \]
Step 3: Find the missing term.
From: \[ 69-25=44 \] Check further: \[ 44-36=8 \] \[ 8-49=-41 \] \[ -41-64=-105 \] Pattern matches perfectly. Thus, the missing term is: \[ \boxed{44} \]
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