Number Sequence Pattern Identification
The question asks us to find the missing number in the sequence: 1, 2, 6, 24, 120, ____. We need to identify the pattern governing this sequence to determine the next term.
Analyzing the Sequence Terms
Let's look at the given numbers:
- Term 1: 1
- Term 2: 2
- Term 3: 6
- Term 4: 24
- Term 5: 120
Finding the Pattern Rule
We can examine the relationship between consecutive terms:
- Term 2 from Term 1: $1 \times 2 = 2$
- Term 3 from Term 2: $2 \times 3 = 6$
- Term 4 from Term 3: $6 \times 4 = 24$
- Term 5 from Term 4: $24 \times 5 = 120$
The pattern observed is that each term is generated by multiplying the previous term by an integer, and this integer increases by 1 for each subsequent step (multiplying by 2, then 3, then 4, then 5).
This sequence is also recognizable as the sequence of factorials:
- $1! = 1$
- $2! = 2 \times 1 = 2$
- $3! = 3 \times 2 \times 1 = 6$
- $4! = 4 \times 3 \times 2 \times 1 = 24$
- $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$
Calculating the Missing Term
Following the identified pattern, the next multiplier should be 6.
We multiply the last term (120) by 6:
Calculation: $120 \times 6 = 720$
Alternatively, using the factorial pattern, the next term is $6!$:
Calculation: $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$
Therefore, the missing number in the sequence is 720.
Important Questions from Sequence & Series
4 is related to 64 following a certain logic. Following the same logic, 9 is related to 729. To which of the following is 12 related following the same logic?
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/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.)What should come in place of ? in the given series based on the English alphabetical order?
ACE, FHJ, KMO, PRT, ?
Which of the following numbers will replace the question mark (?) in the given series?
3, 17, 83, 329, ?, 1961
Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given 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.)
Find the area (in cm²) of the sector, where the radius of the circle is 24 cm and length of the arc is 7 cm.
