Question:
What is the missing number in the following sequence?
\[
0,\ 15,\ 80,\ \_ \_ \_ \_,\ 624
\]
What is the missing number in the following sequence?
\[ 0,\ 15,\ 80,\ \_ \_ \_ \_,\ 624 \]
\[ 0,\ 15,\ 80,\ \_ \_ \_ \_,\ 624 \]
Show Hint
In number series, try to check powers when the numbers grow very fast.
Updated On: Jul 4, 2026
- \(95\)
- \(110\)
- \(205\)
- \(255\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
We observe the sequence: \[ 0,\ 15,\ 80,\ _ _ _ _ ,\ 624 \] These numbers can be written as one less than fourth powers.
Step 1: Check the first term. \[ 1^4-1=1-1=0 \]
Step 2: Check the second term. \[ 2^4-1=16-1=15 \]
Step 3: Check the third term. \[ 3^4-1=81-1=80 \]
Step 4: Find the missing term. The missing term should be \[ 4^4-1 \] \[ =256-1 \] \[ =255 \]
Step 5: Verify the last term. \[ 5^4-1=625-1=624 \] So the pattern is correct.
Step 6: Final answer. \[ \boxed{255} \]
We observe the sequence: \[ 0,\ 15,\ 80,\ _ _ _ _ ,\ 624 \] These numbers can be written as one less than fourth powers.
Step 1: Check the first term. \[ 1^4-1=1-1=0 \]
Step 2: Check the second term. \[ 2^4-1=16-1=15 \]
Step 3: Check the third term. \[ 3^4-1=81-1=80 \]
Step 4: Find the missing term. The missing term should be \[ 4^4-1 \] \[ =256-1 \] \[ =255 \]
Step 5: Verify the last term. \[ 5^4-1=625-1=624 \] So the pattern is correct.
Step 6: Final answer. \[ \boxed{255} \]
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