57 58 62 71 87 112 ?
Number Series Pattern Analysis
We are asked to find the missing term in the number series: 57, 58, 62, 71, 87, 112, ?
To solve this, let's analyze the differences between consecutive terms in the series:
- The difference between the second term (58) and the first term (57) is $58 - 57 = 1$.
- The difference between the third term (62) and the second term (58) is $62 - 58 = 4$.
- The difference between the fourth term (71) and the third term (62) is $71 - 62 = 9$.
- The difference between the fifth term (87) and the fourth term (71) is $87 - 71 = 16$.
- The difference between the sixth term (112) and the fifth term (87) is $112 - 87 = 25$.
Let's examine the sequence of these differences: 1, 4, 9, 16, 25.
We can observe that these differences are perfect squares:
- $1 = 1^2$
- $4 = 2^2$
- $9 = 3^2$
- $16 = 4^2$
- $25 = 5^2$
The pattern indicates that the difference between consecutive terms is the square of the position of the term in the difference sequence (starting from 1).
Calculating the Next Term
Following this pattern, the next difference should be the square of 6, which is $6^2 = 36$.
To find the missing term (the seventh term in the original series), we add this next difference (36) to the last known term (112):
Missing Term = Last Term + Next Difference
Missing Term = $112 + 36$
Missing Term = $148$
Therefore, the number that should come in place of the question mark (?) in the given series is 148.
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.
