801 800 792 765 701 ?
Series Analysis
The task is to determine the missing number in the sequence: 801, 800, 792, 765, 701, ?
We need to find the underlying pattern governing this number series.
Difference Pattern
Let's calculate the differences between consecutive terms:
- $801 - 800 = 1$
- $800 - 792 = 8$
- $792 - 765 = 27$
- $765 - 701 = 64$
The sequence of differences is 1, 8, 27, 64.
Recognizing these numbers:
- $1 = 1^3$
- $8 = 2^3$
- $27 = 3^3$
- $64 = 4^3$
The pattern involves subtracting the cubes of consecutive integers ($1^3, 2^3, 3^3, 4^3$) from the preceding term.
Finding the Missing Number
To find the term replacing the question mark, we continue the established pattern. The next cube in the sequence is $5^3$.
$5^3 = 5 \times 5 \times 5 = 125$
We subtract this value from the last known term (701):
Missing Number = $701 - 125$
Missing Number = $576$
Series Progression
Here's a summary of the series progression:
| Term | Difference (Cube) | Next Term |
|---|---|---|
| 801 | $- 1^3$ ($-1$) | 800 |
| 800 | $- 2^3$ ($-8$) | 792 |
| 792 | $- 3^3$ ($-27$) | 765 |
| 765 | $- 4^3$ ($-64$) | 701 |
| 701 | $- 5^3$ ($-125$) | 576 |
Thus, the number 576 correctly completes the given series.
Important Questions from Number Series
- In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 676 :: 17 : Y - Which of the following options should come in place of the question mark (?) in the given series to make it logically complete?
125, 128, 133, 140, 149,? - What should come in place of the question mark (?) in the given series?
101 110 121 134 149 ? - What should come in place of the question mark (?) in the given series?
40, 48, 58, 66, 76, ? In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down
the numbers into their constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
37, 62
52, 77
